How many cubic feet of each type of gravel are in the truck?

Question

A landscape designer uses two types of gravel for walkways. The larger gravel weighs an average of 48 pounds per cubic foot and thge smaller weighs an average of 40 pounds per cubic foot. In his truck, the designer has a 12-cubic foot load of gravel that weighs 520 pounds. If so, how many cubic feet of each type of gravel are in the truck?

Answer 1

Hi Aubree, you can solve this type of problem using a system of equations. Let l represent the large gravel and s represent the small gravel.

 

Equation 1, amount of each type of gravel:

 

l + s = 12, the sum of the amount of each type of gravel equals the amount the truck can carry.

 

Equation 2, weight of each type of gravel:

 

48 * l + 40 * s = 520.

 

System of equations:

 

    l  +    s  =   12

48l  + 40s  = 520

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You can solve this system by either substitution or elimination. I would suggest you use substitution substituting for s, s = 12 - l, in the second equation.

 

Questions?