Question

Harriet has some five dollar bills and some one dollar bills She has 20 bills. The value of the bills is $72 write and solve a system of equations using elimination to find out how many of each bill she has.
Show your work please. should equal 7 one dollar bills and 13 five dollar bills. Also use ALGEBRA.

Answer 1

So let's say
x=number of five dollare bills
y=number of 1 dolar bills

20 bills total
x+y=20

totla is 72 monies
72=5 times x+1 times y=5x+1y=5x+y
solve

x+y=20
5x+y=72
from here you could do 2 things: go to option 1 (longer) or option 2 (shorter)

1.

 x+y=20
subtract x from both sides
y=20-x

5x+y=72
subtract 5x from boths ides
y=72-5x
subsitute

y=20-x=y=72-5x
20-x=72-5x
add 5x to both sides
20+4x=72
subtract 20 from both sides
4x=52
divide both sides by 4
x=13

subsitute
x+y=20
13+y=20
subtract 13
y=7





2.


 another way is when you got 5x+y=72 and x+y=20
you negative the second equaiton and add to th efirst
I know it sounds like voodo at first but it works
-(x+y=20)=-x-y=-20
add


5x+y=72
-x-y=-20 +
4x+0y=52
4x=52
divide both sides by 4
x=13

subsitute
x+y=20
13+y=20
subtract 13
y=7