Question

a landscaping company mixes its own proprietary blend of topsoil that costs $29.15 per ton to make. the blend contains soil that costs $27.65 per ton and organic compost that costs $42.65 per ton. if the company already has 18 tons of soil on hand, how many tons of compost do they need to mix in? write your answer as a whole number or as a decimal rounded to the nearest tenth. tons

Explanation:

Step1: Set up the equation

Let \(x\) be the tons of compost. The cost of soil is \(27.65\times18\), the cost of compost is \(42.65x\), and the total cost of the blend is \(29.15\times(18 + x)\). So the equation is \(27.65\times18+42.65x=29.15\times(18 + x)\).

Step2: Expand the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(29.15x\) from both sides: \(497.7 + 42.65x-29.15x=524.7+29.15x-29.15x\), which gives \(497.7+13.5x=524.7\). Then subtract \(497.7\) from both sides: \(13.5x=524.7 - 497.7\), so \(13.5x = 27\). Divide both sides by \(13.5\): \(x=\frac{27}{13.5}=2\).

Answer:

\(2\)