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 ?

Mr. Martinson is building a concrete patio in his backyard and decidin

1.	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 ?
Answer» `xle6` `xge6` `xle7.3` `xge7.3` Solution :The total cost y, in dollars, of buying the materials and RENTING the tools for x days from Store A and Store B is found by substituting the respective values for these stores from the table into the GIVEN equation, y = M + (W + K)x, as shown below. Store A :` y =750+( 15 +65 )x= 750+80 x` Store B:`y =600 + ( 25 + 80 ) x= 600 + 105 x ` Thus, the number of days, x, for which the total cost of buying the materials and renting the tools from Store B is less than or equal to the total cost of buying the materials and renting the tools from Store A can be found by solving the inequality `600 + 105x le 750 + 70x`. Subtracting 80x and 600 from each side of `600 + 105x le 750 + 70x` and combining like terms YIELDS `25X le 150`. Dividing each side of `25x le 150` by 25 yields `x le 6`. Choice B is incorrect. The inequality x ge 6 is the number of days for which the total cost of buying the materials and renting the tools from Store B is greater than or equal to the total cost of buying the materials and renting the tools from Store A. Choices C and D are incorrect and may be the result of an error in setting up or simplifying the inequality.

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