SOLUTION: In Jacks piggy bank, there is a collection of pennies, nickels, dimes, and quarters which amounts to $2.87. The number of quarters is one less than twice the number of nickels. The
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Question 1176182: In Jacks piggy bank, there is a collection of pennies, nickels, dimes, and quarters which amounts to $2.87. The number of quarters is one less than twice the number of nickels. There are 4 more pennies than nickels. The number of dimes is twice the number of pennies. How many coins of each kind are there?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
You could solve this using 4 variables, one for the number of each type of coin. But I think it is far easier if you take the time to understand the given information to set up the problem using a single variable. Then you will have a single equation to solve, rather than a system of 4 equations with 4 variables.
The way I read the given information, it will be easiest to use the number of nickels as our variable. So
x = number of nickels
2x-1 = number of quarters (1 less than twice the number of nickels)
x+4 = number of pennies (4 more than the number of nickels)
2(x+4) = 2x+8 = number of dimes (twice the number of pennies)
Use those expressions and the value of each kind of coin to write and solve an equation that says the total value of the coins is $2.87, or 287 cents:
5(x)+25(2x-1)+1(x+4)+10(2x+8) = 287
5x + 50x-25 + x+4 + 20x+80 = 287
76x+59 = 287
76x = 228
x = 3
ANSWERS: The number of each type of coin is
nickels: x = 3
quarters: 2x-1 = 5
pennies: x+4 = 7
dimes: 2x+8 = 14
CHECK: 3(5)+5(25)+7(1)+14(10) = 15+125+7+140 = 287
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
q,d,n,p
Quarters, Dimes, Nickels, Pennies
---------These coin equations are all written in terms of p.
The money equation as cents:
Substitute for each coin other than p:
---------One equation in terms of just variable p.
Simplify
.
.
.
-
(!)
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