Question

Greg combined different weights of fertilizer, soil, and compost to make 29 kilograms (kg) of potting soil for some plants. The weight of fertilizer was x kg. The weight of soil was 2 kg more than three times the weight of fertilizer, and the weight of compost was half the weight of fertilizer. This is represented in the equation below.

x + (3x + 2) + x = 29
What was the difference in the weights of soil and compost Greg combined?
Answer
17 kg
3 kg
6 kg
14 kg

Answer 1

17 kilograms

( thin is an abbreviation for the long one)

Answer 2

These are the things you need to consider first:
"The weight of fertilizer was x kg" - this means that x = weight of the fertilizer
"The weight of soil was 2 kg more than three times the weight of fertilizer" - this means that 3x+2 = weight of soil
"the weight of compost was half the weight of fertilizer." - this means that x/2 = weight of compost

Now we need to plug all of these into this equation:
x + (3x + 2) + x/2 = 29 (we can multiply everything by 2 to get rid of the fraction)
2x + 2(3x+2) + x = 58
2x + 6x + 4 + x = 58
9x + 4 = 58
9x = 58-4
9x = 54
x = 6

This means that the weight of fertilizer is 6kg. That means that the weight of the soil is 3x+2 = 3*6 + 2 = 18+2 = 20kg. That means that the weight of the compost is x/2 = 6/2 = 3kg.

The question was what is the difference in the weights of soil and compost. To get that, we need to subtract 3 from 20: 20 - 3 = 17. The difference in the weights of soil and compost Greg combined is 17kg.