MATH SOLVE

3 months ago

Q:
# Callie and Madison went to buy concert tickets for themselves and their five friends. Thetickets for the closest section were $45 each, and $30 for each ticket in the other section. Theyended up spending a total of $210. How many tickets of each type did they buy?

Accepted Solution

A:

Answer:They bought 0 ticket of closest section and 7 tickets of other sectionStep-by-step explanation:- Callie and Madison went to buy concert tickets for themselves and their five friends- That mean they are 7 - Tickets for the closest section were $45 each- Tickets for other section were $30 each- They ended up spending a total of $210- Assume that they buy x tickets for closest section and y tickets for the other section∵ They want 7 tickets ∴ x + y = 7 ⇒ (1)∵ The cost of the closest section ticket was $45∵ The cost of the other section ticket was $30∵ They spent $210 on them∴ 45x + 30y = 210 - All terms have common factor 15, then divide them by 15∴ 3x + 2y = 14 ⇒ (2)* Now we have a system of equations to solve- Multiply equation (1) by -2 to eliminate y∴ -2x - 2y = -14 ⇒ (3)- Add equations (2) and (3)∴ x = 0- substitute the value of x in equation (1) to find y∴ 0 + y = 7∴ y = 7∵ x represents the number of tickets of the closest section and y represents the number of tickets in the other section∴ They bought 0 ticket of closest section and 7 tickets of other section