Solving a Ratio Problem with Three Variables
$begingroup$
A question that just popped in my head after reading an article:
If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of Planet Y in terms of Earth radii?
I'm having trouble trying to figure this one out. How would we solve this one?
I understand we may have to define one variable in terms of another to get the desired result, but again, I seem to be failing miserably at it.
ratio
asked Nov 12 '15 at 4:02
TRXTRX
43
$endgroup$
add a comment |
$begingroup$
A question that just popped in my head after reading an article:
If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of Planet Y in terms of Earth radii?
I'm having trouble trying to figure this one out. How would we solve this one?
I understand we may have to define one variable in terms of another to get the desired result, but again, I seem to be failing miserably at it.
ratio
asked Nov 12 '15 at 4:02
TRXTRX
43
$endgroup$
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11
add a comment |
$begingroup$
A question that just popped in my head after reading an article:
If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of Planet Y in terms of Earth radii?
I'm having trouble trying to figure this one out. How would we solve this one?
I understand we may have to define one variable in terms of another to get the desired result, but again, I seem to be failing miserably at it.
ratio
asked Nov 12 '15 at 4:02
TRXTRX
43
$endgroup$
A question that just popped in my head after reading an article:
If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of Planet Y in terms of Earth radii?
I'm having trouble trying to figure this one out. How would we solve this one?
I understand we may have to define one variable in terms of another to get the desired result, but again, I seem to be failing miserably at it.
ratio
ratio
asked Nov 12 '15 at 4:02
TRXTRX
43
asked Nov 12 '15 at 4:02
TRXTRX
43
edited Nov 12 '15 at 4:07
TRX
asked Nov 12 '15 at 4:02
TRXTRX
43
asked Nov 12 '15 at 4:02
TRXTRX
43
asked Nov 12 '15 at 4:02
TRXTRX
43
43
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11
add a comment |
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then
$X = 1.16E$
and
$X = 1.40Y$
Substitution gives you $1.16E = 1.40Y$
Solve that equation for $Y$ and you'll have the result that you're looking for.
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
$endgroup$
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
add a comment |
$begingroup$
We have $X = 1.16E$ and $X= 0.4Y$.
Equating these we get $1.16E = 0.4 Y implies Y = frac{1.16}{0.4}E = 2.9E$.
So the radius of planet $Y$ is $2.9$ Earth radii.
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1525254%2fsolving-a-ratio-problem-with-three-variables%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then
$X = 1.16E$
and
$X = 1.40Y$
Substitution gives you $1.16E = 1.40Y$
Solve that equation for $Y$ and you'll have the result that you're looking for.
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
$endgroup$
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
add a comment |
$begingroup$
Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then
$X = 1.16E$
and
$X = 1.40Y$
Substitution gives you $1.16E = 1.40Y$
Solve that equation for $Y$ and you'll have the result that you're looking for.
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
$endgroup$
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
add a comment |
$begingroup$
Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then
$X = 1.16E$
and
$X = 1.40Y$
Substitution gives you $1.16E = 1.40Y$
Solve that equation for $Y$ and you'll have the result that you're looking for.
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
$endgroup$
Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then
$X = 1.16E$
and
$X = 1.40Y$
Substitution gives you $1.16E = 1.40Y$
Solve that equation for $Y$ and you'll have the result that you're looking for.
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
edited Nov 12 '15 at 4:20
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
answered Nov 12 '15 at 4:12
G. AllenG. Allen
1564
1564
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
add a comment |
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
x is 16% larger, not 16% of total.
$endgroup$
– fleablood
Nov 12 '15 at 4:15
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies.
$endgroup$
– TRX
Nov 12 '15 at 4:18
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
$begingroup$
Easy enough to fix. I edited my post to reflect the new wording.
$endgroup$
– G. Allen
Nov 12 '15 at 4:20
1
1
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
$begingroup$
Shouldn't that be X = 0.4Y?
$endgroup$
– TRX
Nov 12 '15 at 4:22
add a comment |
$begingroup$
We have $X = 1.16E$ and $X= 0.4Y$.
Equating these we get $1.16E = 0.4 Y implies Y = frac{1.16}{0.4}E = 2.9E$.
So the radius of planet $Y$ is $2.9$ Earth radii.
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
$endgroup$
add a comment |
$begingroup$
We have $X = 1.16E$ and $X= 0.4Y$.
Equating these we get $1.16E = 0.4 Y implies Y = frac{1.16}{0.4}E = 2.9E$.
So the radius of planet $Y$ is $2.9$ Earth radii.
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
$endgroup$
add a comment |
$begingroup$
We have $X = 1.16E$ and $X= 0.4Y$.
Equating these we get $1.16E = 0.4 Y implies Y = frac{1.16}{0.4}E = 2.9E$.
So the radius of planet $Y$ is $2.9$ Earth radii.
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
$endgroup$
We have $X = 1.16E$ and $X= 0.4Y$.
Equating these we get $1.16E = 0.4 Y implies Y = frac{1.16}{0.4}E = 2.9E$.
So the radius of planet $Y$ is $2.9$ Earth radii.
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
answered Oct 1 '18 at 9:11
MRobinsonMRobinson
1,759319
1,759319
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1525254%2fsolving-a-ratio-problem-with-three-variables%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
I literally just realized that and removed it. You beat me to it!
$endgroup$
– TRX
Nov 12 '15 at 4:07
$begingroup$
Also, I have since reworded the problem accordingly.
$endgroup$
– TRX
Nov 12 '15 at 4:11