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.

Answer 1

Points are earned as:

• 4 points per $ spent on flights
• 2 points per $ spent at hotels
• 1 point per $ spent on all other purchases

Total money spent on credit card last year = $9,480

Total points earned through credit card last year = 14,660 points

Money spent on flight = 140 + 2 × Money spent on hotels

Let money spent on flights be 'a', money spent on hotels be 'b' and money spent on other things be 'c'

⇒ Total money spent on credit card last year = a + b + c = 9,480 ........ (i)

And, Total points earned through credit card last year = 4×a + 2×b + c = 14,660 ........... (ii)

Also, a = 140 + 2×b ............. (iii)

Substitute (iii) in (i) and (ii)

(i): 140 + 2b + b + c = 9,480

⇒ 140 + 3b + c = 9,480

⇒ 3b + c = 9,340 .......... (iv)

(ii): 4×(140 + 2b) + 2b + c = 14,660

⇒ 560 + 8b + 2b + c = 14,660

⇒ 10b + c = 14,100 ....... (v)

Subtracting (iv) from (v)

7b = 4,760

⇒ b = 680

Substituting value of b in (iii)

a = 140 + 2×680

⇒ a = 1,500

Substituting value of 'a' and 'b' in (i)

1,500 + 680 + c = 9,480

⇒ c = 7,300

Hence, Caleb spent $680 on flights, $1,500 on hotels and $7,300 on other purchases