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2 equations using substitutions to solve

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2 Answers

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 :)
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