Question

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies ($0.01). If there are twice as many pennies as nickels and one and a half time the number of nickels as dimes and 34 more pennies than quarters, how many pennies do you have? A. 17 B. 34 C. 42 D. 44

Answer 1

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes  be 'x'.

Let the number of nickels  be '$\dfrac{3}{2}x$'.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$

So, the number of pennies is given by

$3x=3\times 14=42$

Hence, Option 'c' is correct.