Question

Caleb earns points on his credit card that he uses toward future puchases. 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

Caleb spent $1,500 on flights, $680 on hotels, and $7,300 on other purchases, by solving the system of equations derived from the credit card points system.

Step-by-step explanation:

We are asked to determine the amount of money Caleb spent on flights, hotels, and other purchases. Let's denote the money spent on hotels as H, on flights as F, and on other purchases as O. Given that Caleb earns four points per dollar on flights, two points per dollar at hotels, and one point per dollar on all other purchases, we can write down the following equations based on the information provided:

1. 4F + 2H + O = 14,660 (Total points earned)
2. F + H + O = 9,480 (Total amount charged)
3. F = 2H + 140 (Amount spent on flights is $140 more than twice the amount spent on hotels)

Now, we can solve the above system of equations to find H, F, and O. By substituting the third equation into the second and first equations, we eliminate F and solve for H:

2H + 140 + H + O = 9,480

3H + O = 9,340

Now, substituting for F in the points equation:

4(2H + 140) + 2H + O = 14,660

8H + 560 + 2H + O = 14,660

10H + O = 14,100

We now have two equations with two unknowns:

1. 3H + O = 9,340
2. 10H + O = 14,100

Subtracting the two equations, we find:

7H = 4,760

H = 680

Now, we can calculate F and O:

F = 2(680) + 140 = 1,500

O = 9,480 - F - H = 9,480 - 1,500 - 680 = 7,300

We arrive at the final amounts spent: Caleb spent $1,500 on flights, $680 on hotels, and $7,300 on other purchases.