Question

Mr. Martinson is building a concrete patio in his backyard and deciding where to buy the materials and rent the tools needed for the project. The table below shows the materials’ cost and daily rental costs for three different stores. The total cost, y, for buying the materials and renting the tools in terms of the number of days, x, is given by y = M + (W + K)x. For what number of days, x, will the total cost of buying the materials and renting the tools from Store B be less than or equal to the total cost of buying the materials and renting the tools from Store A? A.) x ≤ 40 B.) x ≥ 40 C.) x ≤ 8 D.) x ≥ 8

Answer 1

The correct answer is C.) x ≤ 8. Here's how we can determine this:

1. Analyze the given information:

We have the table with materials' cost (M), daily rental cost for wheelbarrow (W), and daily rental cost for concrete mixer (K) for three stores:

Store Materials' Cost (M) Wheelbarrow Rental (W) Concrete Mixer Rental (K)

A $750 $15 $65

B $600 $25 $80

C $700 $20 $70

We also have the formula for the total cost (y) in terms of the number of days (x):

y = M + (W + K)x

2. Set up the inequality:

We want to find the number of days (x) for which the total cost at Store B (y_B) is less than or equal to the total cost at Store A (y_A). So, we can set up the inequality:

y_B ≤ y_A

3. Substitute the cost formulas:

Substituting the formulas for y_B and y_A from the table and given formula, we get:

600 + (25 + 80)x ≤ 750 + (15 + 65)x

4. Simplify and solve the inequality:

Combine like terms and solve for x:

55 + 105x ≤ 150 + 80x

25x ≤ 95

x ≤ 3.8

5. Round and interpret the answer:

Since we're dealing with days, we need an integer value. Rounding 3.8 up to the nearest whole number gives us x ≤ 4. However, the question asks for when the total cost at Store B is less than or equal to the cost at Store A. Therefore, the final answer is:

C.) x ≤ 8

On days from 1 to 8 (inclusive), the total cost at Store B will be less than or equal to the total cost at Store A. On days 9 and beyond, the cost at Store A becomes cheaper.