Question

1) Ben has 15 coins, all dimes and quarters, worth $2.55. How

many dimes and how many quarters does Ben have?

Answer 1

Ben has 8 dimes and 7 quarters.

Explanation:

Given that:

Number of coins = 15

Worth of coins = $2.55 = 2.55 * 100 = 255 cents

Let,

x be the number of dimes

y be the number of quarters

According to given statement,

x+y=15 Eqn 1

10x+25y=255 Eqn 2

Multiplying Eqn 1 by 10

10(x+y=15)

10x+10y=150 Eqn 3

Subtracting Eqn 3 from Eqn 2

(10x+25y)-(10x+10y) = 255 - 150

10x+25y-10x-10y=105

15y=105

Dividing both sides by 15

`(15y)/(15)=(105)/(15)\\y=7\\`

Putting y=7 in Eqn 1

x+7=15

x=8

Hence,

Ben has 8 dimes and 7 quarters.