Question

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 by using systems of equations with three variables.

Answer 1

Given:
Flights: 4 points per dollar
Hotels: 2 points per dollar
Other: 1 point per dollar.
Total spent = $9,480
Points earned = 14,660

Let
x = money spent on flights
y = money spent on hotels
z = money spent on other purchases.

Because the money spent on flights was $140 more than twice the money spent on hotels, therefore
x = 2y + 140          (1)

Total charges were $9,480, therefore
x + y + z = 9480    (2)

Total points earned was 14,660. Therefore
4x + 2y + z = 14660   (3)

Subtract (2) from (3).
4x + 2y + z - (x + y + z) = 14660 - 9480
3x + y = 5180             (4)
Substitute (1) into (4).
3(2y + 140) + y = 5180
7y + 420 = 5180
7y = 4760
y = 680
From (1), obtain
 x = 2y + 140 = 2*680 + 140 = 1500
From (2), obtain
 z = 9480 - (x + y) = 9480 - (1500 + 680) = 7300

Answer:
$1,500 was spent on flights,
$680 was spent on hotels,
$7,300 was spent on other purchases.