Question

Please help with this question ( math ) !

Answer 1

The number of pennies, which is also equal to the number of dimes is
`\mbox{\large \boxed{15}}` . The number of quarters is
`\mbox{\large \boxed{10}}`

Explanation:

Let the number of pennies = x,

Then number of dimes = x (same as number of pennies)

Let number of quarters = y

Total number of coins = x + x + y = 40

2x + y = 40

The value of each coin is the denomination of each coin multiplied by the number of coins

x pennies = $ 0.01x
x dimes = $0.10x

y quarters = $0.25y

Total value = 0.01x + 0.10x + 0.25y = 4.15

= 0.11x + 0.25y = 4.15

Multiply above equation by 4 so the Q term matches that of equation (1)

4(0.11x + 0.25y) = 4 x 4.15

0.44x + 1y = 16.6 (2)

Subtract: Eq(1) - Eq(2):
(2x + y = 40) - (0.44x + y =16.6)

=> 2x+ y (0.44x + y) = 40 - 16.6
=> 2x - 0.44x + y - y = 23.4
=> 1.56x = 23.4

x= 23.4/1.56 = 15

So there are 15 dimes and hence 15 pennies

Since total number of coins is 40
15 + 15 + y = 40

y = 40 - 30 = 10

Hence there are 15 pennies, 15 dimes and 10 quarters

In case you need to fill up the table also here it is

Denomination Number of Coins Value
--------------------------------------------------------------------
0.01 x 0.01x
0.10 x 0.10x
0.25 y 0.25y

----------------------------------------------------------------------
40 4.15