Question 1047705
let q equal the number of quarters and let 25 * q equal the value of the quarters in cents.


for example, if q = 1, then the value is equal to 25 * 1 = 25 cents.


let d equal the number of dimes and let 10 * d equal the value of the dimes in cents.


you are given that the jar contains 5 more quarters than it has dimes.


this means that q = d + 5.


if you have 1 dime, than you have 6 quarters.
if you have 2 dimes, then you have 7 quarters.
you always have 5 more quarters than dimes, based on this equation.


the value in the jar is going to be 25 * q + 10 * d and that value is going to be equal to 6 dollars and 15 cents.


since 1 dollar is equal to 100 cents, then 6 dollars and 15 cents is equal to 615 cents.


your equation for that is 25 * q + 10 * d = 615


from the first equation, you know that q = d + 5, so you can replace q with d + 5 in the second equation to get:


25 * (d + 5) + 10 * d = 615


simplify this equation to get:


25 * d + 125 + 10 * d = 615


subtract 125 from both sides of the equation to get:


25 * d + 10 * d = 615 - 125


combine like terms to get:


35 * d = 490


solve for d to get:


d = 490 / 35 = 14


the jar contains 14 dimes.


since it contains 5 more quarters than dimes, the jar also contains 19 quarters.


19 * 25 + 14 * 10 = 475 + 140 = 615 cents


615 cents / 100 = 6 dollars and 15 cents which can be shown as 6.15