Answer:
Ben has 8 dimes and 7 quarters.
Step-by-step 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
[tex]\frac{15y}{15}=\frac{105}{15}\\y=7\\[/tex]
Putting y=7 in Eqn 1
x+7=15
x=8
Hence,
Ben has 8 dimes and 7 quarters.
