Two customers each purchase towels and washcloths from a home goods store. Each towel costs the same amount, and each washcloth
costs the same amount.
• Customer 1 pays $34.80 for 8 towels and 4 washcloths.
• Customer 2
pays
12 towels and 8 washcloths.
$55.20 for
What is the cost, in dollars and cents, of each washcloth?

towel: 3.60 ; washcloth: 1.50

Step-by-step: X represents the number of towels. Y represents the number of washcloths.

8x + 4y = 34.80

12x + 8y = 55.20

16x + 8y = 69.60

4x = 14.40

x = 3.60

y = 1.50

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3