Question

5. Caleb earns points on his credit card that he can use towards future purchases. He earns four

points per dollar spent on flights, two points per dollar spent at hotels, and one point per
dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned
14,660 points. The amount of money spent on flights was $140 more than twice the amount
of money spent on hotels. Find the amount of money spent on each type of purchase.

Answer 1

To find the amount of money spent on flights and hotels, set up equations using given information. Solve the equations to find that any amount of money can be spent on flights and hotels.

Step-by-step explanation:

To find the amount of money spent on each type of purchase, let's set up the equations:

Let x = amount of money spent on flights

Let y = amount of money spent on hotels

We are given:

x + y + (9480 - x - y) = 9480

x + y + 9480 - x - y = 9480

9480 = 9480

So one of the equations is satisfied.

We are also given:

4x + 2y + (140 + 2y) + (14,660 - 4x - 2y - 140 - 2y) = 14,660

4x + 2y + 140 + 2y + 14,660 - 4x - 2y - 140 - 2y = 14,660

4y - 4y + 140 - 140 = 14,660 - 14,660 - 2y - 2y

0 = -4y

0 = 0

The second equation is automatically satisfied, so there are no constraints on the amount of money spent on flights and hotels.

Therefore, any amount of money can be spent on flights and hotels.