Question 120041: Find the value of the change in a purse that contains 4 times as many nickels as pennies, 2 more dimes than nickels, and 5 more quarters than dimes and nickels combined. Express your answer in terms of p, the number of pennies.
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Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find the value of the change in a purse
Let
p = no. of pennies
n = no. of nickels
d = no. of dimes
q = no. of quarters
:
Write an equation for each statement:
:
"that contains 4 times as many nickels as pennies,"
n = 4p
:
"2 more dimes than nickels,"
d = n + 2
:
"and 5 more quarters than dimes and nickels combined."
q = d + n + 5
:
Express your answer in terms of p, the number of pennies.
:
Using above equations:
:
d = n + 2
d = 4p + 2; substitute 4p for n
:
q = d + n + 5
q = (4p+2) + 4p + 5; substituted (4p+2) for d and 4p for n
q = 8p + 7
:
Find the value of:
pennies + nickels + dimes + quarters =
.01p + .05(4p) + .10(4p+2) + .25(8p+7) =
:
Get rid of all those decimals multiply equation by 100
p + 5(4p) + 10(4p+2) + 25(8p+7) =
:
p + 20p + 40p + 20 + 200p + 175 = 261p + 195 is the value (in cents)
:
I think the method is right, but a a lot of chance for math errors here,
Check my work carefully.
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