Question

adult tickets at a football game cost $6 and student tickets cost $2. A total of $1776 was collected on 372 tickets. How many adult tickets were sold?

Answer 1

Answer:

258

Step-by-step explanation:

Set up the two equations needed (x is the adult tickets and y is the student tickets)

x+y=372

6x+2y=1776

Solve by elimination

-2(x+y=372)

=-2x-2y=-744

Cancel like figures:

-2x-2y=-744

6x+2y=1776

= 4x=1032

x=258

Answer 2

258 adult tickets were sold.
1) Set up your 2 equations
• 6a +2s= $1776 (remember cost of each type of ticket goes with the total cost)
• a+s= 372 (number of tickets goes with the total number of tickets)
2) Easy way is to use your calculator and the matrix option
(first section: two rows/two columns)
(second section: two rows/one column)
•put the first section to the negative 1 power and multiply it by the second section
-> The answer for # of adult tickets are on top and student is on bottom. I have an example on the bottom
Or a second way
1) Set up equations
• 6a+2s=$1776
• s+a= 372
2) Rearrange bottom equation to use substitution method
• a= 372- s
3) Then substitute a with top equation and distribute
• 6(372-s) + 2s= $1776 = 2232-6s + 2s= $1776
4) Add like terms and solve for s
• 2232-4s= $1776
-> minus 2232 from 1176= -456
-> divide -4s by itself and -456
-> number of student tickets are 114
5) Plug in 114 to equation (a=372-s) Then subtract 372- 114 and you get the number of adult tickets! :)
Hopefully this helped <3