Finding Percents

Question

Company A rents cars for $27 per day and 9¢ per mile driven. Company B rents cars for $19 per day and 12¢ per mile driven. You want to rent a car for one day. Find the maximum number of miles you can drive a Company B car if it is to cost you less than a Company A car. (Give your answer as a whole number.)

Answer 1

You will need to use systems of equations to solve this question.

Step 1: use the information to make the linear equations (the initial cost per day is the y-intercept and the cost per mile is the slope).

Company A's daily cost: C(m)= .09m+ 27

Company B's daily cost: C(m)= .12m+ 19

Step 2: use substitution and solve for the variable m.

Company A's cost > Company B's cost

.12m + 19 > .09m+27

12m+190 > 9m+270 multiply each side by 100

3m+190 > 270 subtract 9m from each side

3m > 80subtract 190 from each side

m > 26.667. Therefore one will need to drive more than 27 miles in order for Company B to be cheaper than Company A