2. Tennis rackets can be packaged in cartons holding 2 rackets cach or in cartons holding 3 rackets each. Yesterday's packing slip showed that 38
cartons were used to pack a total of 100 rackets. How many cartons of each
size were used yesterday?

There were 14 cartons of size 2 rackets and 24 cartons of size 3 rackets

Step-by-step explanation:

Assume that the number of cartons holding 2 rackets is x and the number of cartons holding 3 rackets is y

∵ There are x cartons of 2 rackets

∵ There are y cartons of 3 rackets

∵ They used 38 cartons

∴ x + y = 38 ⇒ (1)

∵ They packed a total of 100 rackets

∴ 2x + 3y = 100 ⇒ (2)

Let us solve the system of equations

→ Multiply equation (1) by -2 to make the coefficients of x in

   the equations equal in values and different is signs

∵ -2(x) + -2(y) = -2(38)

∴ -2x - 2y = -76 ⇒ (3)

→ Add equations (2) and (3)

∴ y = 24

→ Substitute the value of y in equation (1) or (2) to find x

∵ x + 24 = 38

→ Subtract 24 from both sides

∴ x + 24 - 24 = 38 - 24

∴ x = 14

There were 14 cartons of size 2 rackets and 24 cartons of size 3 rackets