2 equations using substitutions to solve

Question

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?

Answer 1

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 :)

Answer 2

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