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

"The weight of fertilizer was x kg"


so x = weight of fertilizer


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"The weight of soil was 2 kg more than three times the weight of fertilizer"


So 3x+2 = weight of soil


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"the weight of compost was half the weight of fertilizer.",


So x/2 = weight of compost

Answer 2

To find our answer, we have to solve for x first


x + (3x + 2) + x/2 = 29


2x + 2(3x + 2) + x = 2*29


2x + 6x + 4 + x = 58


9x + 4 = 58


9x = 58-4


9x = 54


x = 54/9


x = 6


So the weight of the fertilizer is 6 kg

Answer 3

Now plug x = 6 into 3x+2 and simplify


3x+2

3(6)+2

18+2

20

So the weight of the soil is 20 kg

Answer 4

Thanks!

Answer 5

And finally, plug x = 6 into x/2 to get


x/2

6/2

3

so we know that the weight of the compost is 3 kg

Answer 6

The last part is to subtract the weights of the compost from the soil to get:

20 - 3 = 17

which is the final answer


you're welcome