Elimination

A customer bought 5 pounds of mango and papaya for $37.75. How many pounds of each fruit did customer buy ? Mango=$8.00/lb Papaya=$7.25

 

Let the number of pounds of mangos=m

Let the number of pounds of papaya=p

m + p =5

8m + 7.25p=37.75

 

Solve the following system:

{8 m+7.25 p = 37.75

m+p = 5

In the second equation, look to solve for p:

{8 m+7.25 p = 37.75

m+p = 5

Subtract m from both sides:

{8 m+7.25 p = 37.75

p = 5-m

Substitute p = 5-m into the first equation:

{7.25 (5-m)+8 m = 37.75

p = 5-m

7.25 (5-m)+8 m = 8 m+(36.25-7.25 m) = 0.75 m+36.25:

{0.75 m+36.25 = 37.75

p = 5-m

In the first equation, look to solve for m:

{0.75 m+36.25 = 37.75

p = 5-m

0.75 m+36.25 = (3 m)/4+145/4 and 37.75 = 151/4:

(3 m)/4+145/4 = 151/4

Subtract 145/4 from both sides:

{(3 m)/4 = 3/2

p = 5-m

Multiply both sides by 4/3:

{m = 2

p = 5-m

Substitute m = 2 into the second equation:

Answer: |{m = 2    and    p=3