Question

A landscaper wants to use a mixture of soil and sand to ensure proper water drainage. He has just 50 cubic meters of soil that is 42% sand and an unlimited quantity of soil that is 22% sand. How many cubic meters of the 22% soil should he add to the 42% to create a mixture that is 36% sand? Write your answer as a whole number or as a decimal rounded to the nearest tenth. cubic meters.

Answer 1

The landscaper needs to add 21.4 cubic meters of 22% sand soil to 50 cubic meters of 42% sand soil to create a mixture that is 36% sand.

Step-by-step explanation:

The question requires solving a mixture problem using algebra to find how many cubic meters of 22% sand soil need to be mixed with 50 cubic meters of 42% sand soil to create a mixture that is 36% sand. Let x represent the number of cubic meters of the 22% sand soil needed.

The equation representing the sand content in the new mixture would be:

0.42(50) + 0.22(x) = 0.36(50 + x)

Solving for x:

21 + 0.22x = 18 + 0.36x

0.14x = 3

x = 3 / 0.14

x = 21.4

So, the landscaper needs to add 21.4 cubic meters of the 22% soil to the 42% soil to achieve a mix that is 36% sand.