Answer:
h ≤ 10
Explanation:
Let's first consider the cost of renting the boat without the discount. If Andy rents the boat for h hours, he will have to pay:
Cost = (price * time)
Cost = 7h
With the $4 discount, the cost of renting the boat for h hours will be:
Cost = (price * time) - discount
Cost = 7h - 4 .
We want to find the possible values of h such that the total cost of renting the boat is at most $66, which means:
7h - 4 ≤ 66
Step 1: To solve for h, we will add 4 to both sides of the inequality:
7h ≤ 70
Step 2: Finally, we will divide both sides by 7 to isolate h:
h ≤ 10
Therefore, Andy can rent the boat for at most 10 hours with his budget of $66 and the $4 discount coupon.
In inequality form, the solution is:
0 < h <= 10
Optional Step 3: We can try plug in 9 for h, 10 for h, and 11 for h to see how the inequality works:
9 for h:
7(9) - 4 ≤ 66
63 - 4 ≤ 66
59 ≤ 66
Thus, normally, the price to boat for 9 hours without the discount is $63, but with the $4 discount its now $59. $59 is less than $66 and allows Andy to not exceed his limit.
10 for h:
7(10) - 4 ≤ 66
70 - 4 ≤ 66
66 ≤ 66
Thus, normally, the price to boat for 10 hours without the discount is $70, but with the $4 discount its now $66. $66 is equal to $66 and is maximum amount Andy can spend to not exceed his limit.
11 for h:
7(11) - 4 ≤ 66
77 - 4 ≤ 66
73 ≤ 66
73 > 66
Thus, normally, the price to boat for 11 hours without the discount is $77, but with the $4 discount its now $73. $73 is greater than to $66 and causes Andy to exceed his limit since 11 is greater than 10.