Question 4912
Let x=number of nickels
let x-3=number of dimes (3 fewer than nickels)
let 2x=number of quarters (twice as many as nickels)


Let 5x=the value of all nickels (5 cents for each nickel)
Let 10(x-3)= the value of all dimes (10 cents for each dime)
Let 25(2x)= the value of all quarters (25 cents for each quarter)


Then adding all values together we know:
$7.50= total value of all coins
We are working in cents, so convert$7.50 to 750 cents and write the equation:
750=5x+10(x-3)+25(2x)


Clear the parentheses:
750=5x+10x-30+50x
Combine like terms:
750=65x-30
Add 30 to both sides:
780=65x
Divide both sides by 65:
12=x

Using our original statments we know their are 12 nickels, 9 dimes (3 fewer than the nickels) and 24 quarters (twice as many as the nickels).

Check your answer:
12 * $.05 = $.60
 9 * $.10 = $.90
24 * $.25 =$6.00

$6.00+.90+.60=$7.50, So this is correct.