Question

One ticket cost $6, and two tickets for a couple cost $10. You sold 196 tickets and gained $1076. How many couples bought tickets?

Answer 1

How many couples bought tickets?

50

Explanation:

s + 2c = 196 Eq. 1

6s + 10c = 1076 Eq, 2

s = single tickets

c = couple tickets

From Eq. 1:

s = 196 - 2c Eq. 3

Replacing Eq. 3 in Eq. 2:

6(196-2c) + 10c = 1076

(6*196 + 6*-2c) + 10c = 1076

(1176 - 12c) + 10c = 1076

1176 - 2c = 1076

1176 - 1076 = 2c

100 = 2c

c = 100/2

c = 50

From Eq. 3:

s = 196 - 2c

s = 196 - 2*50

s = 196 - 100

s = 96

Check:

From Eq. 2:

6s + 10c = 1076

6*96 + 10*50 = 1076

576 + 500 = 1076