SAT Mathematics Practice Test 4

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,$\mathit{y}=\mathit{M}+\left(\mathit{W}+\mathit{K}\right)\mathit{x},$ as shown below.Store $\mathit{A}:\mathit{y}=750+\left(15+65\right)\mathit{x}=750+80\mathit{x}$
$\mathit{S}\mathit{t}\mathit{o}\mathit{r}\mathit{e}\mathit{B}:\mathit{y}=600+\left(25+80\right)\mathit{x}=600+105\mathit{x}$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 $600+105\mathit{x}\le 750+70\mathit{x}.$ Subtracting $80\mathit{x}$ and 600 from each side of $600+105\mathit{x}\le 750+70\mathit{x}$ and combining like terms yields $25\mathit{x}\le 150$.Dividing each side of $25\mathit{x}\le 150$ by 25 yields $\mathit{x}\le 6.$Choice B is incorrect. The inequality x ≥ 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.