Question

Sharon has some one dollar bills and som five dollar bills . She has 14 bills . The value of the bills are $30. Solve a system of equations using elimination to find how many of each kind of bill she has

Answer 1

Let the no. of one dollar bills be x and the no. of five dollar bills be y.

She has 14 bills = > 1st equation => x+y=14
The value of the bills are $30 = > 2st equation => ($1)x + ($5)y = 30

Simultaneous equations :
x + y = 14 => x = 14 - y
x + 5y = 30

Sub x = 14 - y into x + 5y = 30 ,
ie. (14 - y) + 5y = 30 => 14 +4y = 30 => 4y = 16 => y=4

Answer 2

lets x = # of one dollar bills, y = # of five dollars bills

x + y = 14 so x = 14-y
x + 5y = 30
substitute x = 14-y into x + 5y = 30
x + 5y = 30
14 -y + 5y = 30
4y = 16
y = 4

x = 14 - y = 14-4=10

# of one dollars bills = 10 ($1x10 = $10)
# of five dollars bills = 4 ($5 x 4 = 20)

double check
$10+$20 = $30 (The value of the bills are $30)
4+10=14 (She has 14 bills )