Question 1047705: please help me with this question:
The jar has 5 more quarters than it has dimes. If the value of the coins is $6.15, how many quarters are in the jar?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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