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# 2 equations using substitutions to solve

A student has some \$1 bills and some \$5 bills. He has 15 bills totaling \$47. How many of each type of bill does he have and what 2 equations using substitutions can be used to solve them?

### 2 Answers by Expert Tutors

4.9 4.9 (233 lesson ratings) (233)
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Hey Joe -- reasoning: \$47 means having 2 or 7 or 12 ones ... 2 ones leaves 13 fives

-- too big ... 12 ones leaves 3 fives -- too small ==> 7(\$1) + 8(\$5) =  7+40 :)
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Joe;
Here we go again...

x=quantity \$1 bills
y=quantity \$5 bills
FIRST EQUATION...
x + y=15
or
y=15-x
or
x=15-y

SECOND EQUATION...
\$1x + \$5y=\$47
Let's eliminate the \$ for simplicity...
(\$1x+\$5y)(\$)=\$47/\$
It is just as important to eliminate symbols as numbers...
x+5y=47

Let's substitute for x...
x+5y=47
x+5(15-x)=47
x+75-5x=47
75-4x=47
-4x=47-75
-4x=-28
4x=28
x=7

Let's substitute for y...
x+5y=47
(15-y)+5y=47
15+4y=47
4y=32
y=8

Let's test the result of
x=7, quantity of \$1 bills
y=8, quantity of \$5 bills

Does 47= (7)(\$1)+(8)(\$5) ?
47=\$7+\$40=\$47