Question

Pencils cost $7 per carton and erasers cost $4 per carton. If an order comes in for a total of 150 cartons costing $900, what was the specific number of cartons of pencils?

Answer 1

Let cartons of pencils = P and cartons of erasers = E

Total cartons is 150, so you have P + E = 150

Total cost is $900, so you have 7P + 4E = 900

Rewrite the quantity equation as P = 150 - E

Replace P in the cost equation:

7(150 - E) + 4E = 900

Use the distributive property:

1050 - 7E + 4E = 900

Simplify:

1050 - 3E = 900

Subtract 1050 from both sides:

-3E = -150

Divide both sides by -3:

E = -150 / -3

E = 50

There were 50 cartons of Erasers.

Subtract the number of erasers from the total cartons to get the number of cartons of pencils:

150 - 50 = 100 cartons of pencils.