SOLUTION: Hi
I was wondering if I could get a second opinion on this problem. Jack and jill had some money in the ratio of 5 to 2 respectively. They jointly paid for a restaurant bill in th
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I was wondering if I could get a second opinion on this problem. Jack and jill had some money in the ratio of 5 to 2 respectively. They jointly paid for a restaurant bill in th
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Question 1147259: Hi
I was wondering if I could get a second opinion on this problem. Jack and jill had some money in the ratio of 5 to 2 respectively. They jointly paid for a restaurant bill in the ratio of 2 to 1 respectively. If jill spent 1/5 of her money and jack had 126 dollars left, how much did the bill cost.
thanks Answer by greenestamps(13203) (Show Source):
The amounts they started with were Jack:Jill = 5:2, so
let 5x = amount Jack started with
let 2x = amount Jill started with
Note that is a standard way to start on a problem where a ratio of 5:2 is given.
The amounts they paid on the bill were Jack:Jill = 2:1, so
let 2y = what Jack paid
let y = what Jill paid
Jill spent 1/5 of her money:
[1]
Jack had $126 left:
[2]
That's two equations in x and y. Solve by any method you like.
With one equation specifically defining one variable in terms of the other, substitution seems appropriate.
The number that is asked for is the total of the bill (not the "cost of the bill"), which is 2y+y = 3y.
ANSWER: The bill was 3y = $36
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Added after seeing the two responses from other tutors....
Both of the other responses had valid starts on the problem -- both of them very different from each other, and very different from mine. That's a good demonstration of the fact that there are almost always many different ways to set up a problem for solving.
Unfortunately in one of the responses a simple substitution was done incorrectly, leading to a wrong answer. It might be educational to look at the start of that response to see where the error was made and then follow that path to the final correct answer.
