Question 209071
A childs coin bank contains 2.58 in pennies and nickels.
If the number of pennies is 36 less than 2 times the number of nickels,
 how many pennies are in the bank?
:
Let p = no. pennies
let n = no. of nickels
:
Write an equation for each statement:
:
"coin bank contains 2.58 in pennies and nickels."
.01p + .05n = 2.58
Multiply equation by 100 to get rid of the decimals, use cents
1p + 5n = 258
:
"the number of pennies is 36 less than 2 times the number of nickels,"
p = 2n - 36
:
Substitute (2n-36) for p in the cents amt equation
(2n-36) + 5n = 258
2n + 5n = 258 + 36
7n = 294
n = {{{294/7}}}
n = 42 nickels
then
p = 2(42) - 36
p = 84 - 36
p = 48 pennies
:
:
Check solution in original $amt equation
.01(48) + .05(42) = 
.48 + 2.10 = 2.58