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A building contractor is to dig a foundation 42 feet​ long, 18 feet​ wide, and 3 feet deep. The contractor pays ​$20 per load for trucks to remove the dirt. Each truck holds 7 cubic yards. What is the cost to the contractor to have all the dirt hauled​ away?

Respuesta :

notice something? the measurements are in feet while the cost and the loads are in yards

let's convert them using the conversion 1 yard = 3 feet!

1(14) yard = 3(14) feet

14 yards = 42 feet

1(6) yard = 3(6) feet

6 yards = 18 feet

1(1) yard = 3(1) feet

1 yard = 3 feet

now let's find the volume of the foundation (dirt) that need's to be scooped up!

volume = length x width x depth

volume = 14yd x 6yd x 1yd

volume = 84yd^3

each load is  7 cubic yards or 7yd^3 scoops of dirt,

since we got 84 of those we divide it by 7 to see how many loads will fit all 84 yd^3!

84 / 7 = 12 loads!

each load is $20, and we have 12 of those so we multiply the cost by 12 to see the cost for 12 loads!

20 x 12 = $240

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