Question

Mario buys tickets for either 47 or 57 dollars. He purchases 14 tickets and spends 738 dollars. How many tickets did he purchase at each price?

Answer 1

6 tickets were purchased at $47

8 tickets were purchased at $57

Explanation:

Let the tickets purchased at $47 be x

Let the tickets purchased at $57 be y

We can form an equation from the question given which will be:

x + y = 14 ....... i

47x + 57y = 738 ........ ii

From equation i

x = 14 - y ........ iii

Substitute iii into ii

47x + 57y = 738

47(14-y) + 57y = 738

658 - 47y + 57y = 738

Collect like terms

-47y + 57y = 738 - 658

10y = 80

y = 80/10

y = 8

8 tickets were purchased at $57

Note that from i

x + y = 14

x + 8 = 14

x = 14 - 8

x = 6

6 tickets were purchased at $47