Chapter 4, Problem 39CLR

To determine

To find: The number of coins each person have.

Answer to Problem 39CLR

J: 10 dimes and 6 quarters; W: 20 dimes and 3 quarters.

Explanation of Solution

Given information:

Let the number of dimes J has be x

Then number of quarters are 16 − x

As given,

The number of dimes W has is $2x$

And the number of quarters $\frac{1}{3}(16-x)$

Calculation:

Let the number of dimes J has be x

Then number of quarters are 16 − x

As given,

The number of dimes W has is $2x$

And the number of quarters $\frac{1}{3}(16-x)$

As both have same amount of money:

  $10x+25(16-x)=20x+\frac{25}{3}(16-x)$

  $10x-25x+400=\frac{60x+400-25x}{3}$

  $-45x+1200=35x+400$

  $80x=800$

  $x=10$

J has 10 dimes

Then number of quarters that J has will be

  $16-10$

  $=6$

  $\text{W}$ will have,

  $2(10)$ Dimes

  $=20$

And $\frac{1}{3}(6)$

  $=2$ quarters

Hence, J: 10 dimes and 6 quarters; W: 20 dimes and 3 quarters.