Aski rental store rents a pair of skis for $44 a day and a snowboard for $58 a day. yesterday, the store made $2,232 on ski and snowboard rentals. they rented 9 more pairs of skis than snowboards. write a system of equations that could be used to represent this situation and to find the number of ski rentals and snowboard rentals.

First, let the number of skis rented by x and the number of snowboards rented by y. We can then assemble the first equation from the amount of money made from the rentals.

44x + 58y = 2232

The second equation can come from the fact that 9 more skis were rented than snowboards.

y = x - 9

Therefore our system is:

44x + 58y = 2232

y = x - 9

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.