Chapter 3.7, Problem 15P

To determine

To verify: The argument about R’s claim.

Answer to Problem 15P

R’s claim is wrong.

Explanation of Solution

Given information:

Total amount is $20.

Quarters are twice of the half − dollars.

One − dollar bills are half of the half − dollars.

Calculations:

Let x be the number of half − dollars.

Then

	Number	Value (cents)	Total (cents)
Quarters	2x	25	50x
Half − dollars	x	50	50x
Dollars	0. 5x	100	50x

We know that

$1 = 100 cents

Thus,

  $50x+50x+50x=2000$

That becomes

  $150x=2000$

Divide both sides by 150:

  $x=\frac{2000}{150}=13\frac{1}{3}$

Thus,

The number of half - dollars is $13\frac{1}{3}$ .

We know that

  $13\frac{1}{3}$ is not a whole number and it’s impossible for the half − dollars.

This implies

R’s claim must be wrong.