Question

A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?

Answer 1

Let the number of half dollars be x,

number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
= 0.75x + 0.5
0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
= 17

There are 17 quarters and 15 half dollars.

Answer 2

Let the number of half dollars be x,

number of quarters = x + 2

amount of half dollars = 0.5x

amount of quarters = 0.25(x + 2)

= 0.25x + 0.5

total amount = 0.5x + 0.25x + 0.5

= 0.75x + 0.5

0.75x + 0.5 = 11.75

0.75x = 11.25

x = 15

number of quarters = x + 2

= 15 + 2

= 17

There are 17 quarters and 15 half dollars.