SOLUTION: melisa came to the bank to make a deposit of loose change in her checking account. The total she deposited was $10.19. There were 71 coins in total. Those coins being quarters, dim

Question 1002353: melisa came to the bank to make a deposit of loose change in her checking account. The total she deposited was $10.19. There were 71 coins in total. Those coins being quarters, dimes and pennies. The amount of pennies was twice the amount of dimes. How many of each coin is there?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
melisa came to the bank to make a deposit of loose change in her checking account.
Those coins being quarters, dimes and pennies.
let q = no. of quarters
let d = no. of dime
let p = no. of pennies
:
Write an equation for each statement
:
The total she deposited was $10.19.
.25q + .10d + .01p = 10.19
:
There were 71 coins in total.
q + d + p = 71
:
The amount of pennies was twice the amount of dimes.
p = 2d
:
in the two above equations replace p with 2d
.25q + .10d + .01(2d) = 10.19
.25q + .12d = 10.19
and
q + d + 2d = 71
q + 3d = 71
q = -3d + 71
:
Replace q with (-3d+71) in .25q + .12d = 10.19
.25(-3d+71) + .12d = 10.19
-.75d + 17.75 + .12d = 10.19
-.75d + .12d = 10.19 - 17.75
-.63d = -7.56
d = -7.56/-.63
d = +12 dimes
Find the quarters
q = -3(12) + 71
q = 35 quarters
"The amount of pennies was twice the amount of dimes."
p = 2(12)
p = 24 pennies
:
Check to see if all this adds up
.01(24) + .10(12) + .25(35) =
.24 + 1.20 + 8.75 = 10.19
:
How many of each coin is there? 24 pennies, 12 dimes and 35 quarters
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