Callie and Madison went to buy concert tickets for themselves and their five friends. The

tickets for the closest section were $45 each, and $30 for each ticket in the other section. They

ended up spending a total of $210. How many tickets of each type did they buy?

They bought 0 ticket of closest section and 7 tickets of other section

Step-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