Question

A box contains 39 total coins and bills worth $36.60 all coins are either five dollar bills or nickels how many of each type are there?

Answer 1

There are 7 five dollar bills and 32 nickel coins.

Step-by-step explanation:

Given,

Total coins = 39

Worth of coins = $36.60

Nickel = 5 cents = 5/100 = $0.05

Let,

x be the number of nickels

y be the number of five dollar bills

According to given statement;

x+y=39         Eqn 1

0.05x+5y=36.60    Eqn 2

Multiplying Eqn 1 by 5

$5(x+y=39)\\5x+5y=195\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(5x+5y)-(0.05x+5y)=195-36.60\\5x+5y-0.05x-5y=158.40\\4.95x=158.40$

Dividing both sides by 4.95

$\frac{4.95x}{4.95}=\frac{158.40}{4.95}\\x=32$

Putting x=32 in Eqn 1

$32+y=39\\y=39-32\\y=7$

There are 7 five dollar bills and 32 nickel coins.

Keywords: linear equation, elimination method

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