SOLUTION: Hi Tom and John paid for a present in the ratio of 7 to 4 respectively. In doing so John spent a quarter of his money and Tom had $99 left. If the ratio of the amount of Tom's mon

Question 1205512: Hi
Tom and John paid for a present in the ratio of 7 to 4 respectively. In doing so John spent a quarter of his money and Tom had $99 left. If the ratio of the amount of Tom's money to John's money was 5 to 2 respectively before they bought the present, how much did the present cost.
Thanks
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52868)   (Show Source): You can put this solution on YOUR website!
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Tom and John paid for a present in the ratio of 7 to 4 respectively.
In doing so John spent a quarter of his money and Tom had $99 left.
If the ratio of the amount of Tom's money to John's money was 5 to 2 respectively
before they bought the present, how much did the present cost.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

From the problem, Tom paid 7x dollars; John paid 4x dollars, where x is the common measure of their payments. Before spending, John had 4*(4x) = 16x dollars inititially. Before spending, Tom had (7x+99) dollars initially. From the problem, we have this proportion = = . From the proportion 2*(7x+99) = 5*(16x) 14x + 198 = 80x 198 = 80x - 14x 198 = 66x x = 198/66 = 3. The present's cost was 7x+4x = 11x = 11*3 = 33 dollars. ANSWER

Solved.

Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!

The other tutor solved the problem starting from one logical starting point -- the ratio of 7:4 that Tom and John paid for the present.

To be good at algebra, you want to be open to trying different methods for setting up a problem. Often the amount of work required to solve the problem will be very different for different ways of setting the problem up.

So let's just see how the solution looks if we start instead from the ratio 5:2 of the amount Tom and John started with.

Let 5x = amount Tom started with
Let 2x = amount John started with

John spent a quarter of his money, the amount he spent was 0.5x.

Tom finished with $99, so the number of dollars he spent was 5x-99.

The ratio of the amounts they spent was 7:4.

The amount Tom spent was 5x-99 = $21; the amount John spent was 0.5x = $12.

ANSWER: The total cost of the present was $21+$12 = $33.

Same answer as from the other tutor of course....

But in this problem the level of difficulty for solving the problem by the other method for setting up the problem seems less.

But you never know until you try....

And the whole point of my response to your question is to encourage you to always consider the possibility of setting up a problem for solving in different ways.

Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!

PERSON ORIGINAL SPENT REMAINING MONEYS Tom t x 99 John j j/4 3j/4

Ratio tom to john before any spending

Ratio of money remaining for each after spending

Tom's remaining money, 99.

System of equations

.
.

Substituting for t,
.
.

.
.

What the present cost:

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