Question

For the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,664. How many adult tickets and how many senior tickets were sold?
?= adult tickets ?= senior tickets

Answer 1

We can take adult ticket as x and senior ticket as y.

Now we will form two equations

x + y = 140

13x + 10y = 1664

This system of equations we will solve using Gaussian algorithm (gradual elimination of the variables)  

We will multiply first equation with (-10) and get

-10x-10y=-1400 Than we will add to second equation and get

3x=264 => x=264/3=88 => x=88

Now we will replace x in the first equatin before multiplying and get

88+ =140 => y= 140-88= 52 => y=52

adult tickets x=88  and senior tickets y=52

Good luck!!!

Answer 2

Answer:

88 adult tickets, 52 senior tickets

Step-by-step explanation:

Write the equation by adding the total values of each type of ticket.

13a+10(140−a)=1,664

We can solve this equation for a  to find the number of adult tickets sold.

13a+10(140−a)=1,664

13a−10a+1,400=1,664

3a=1,664

3a=264

a=88

So, the number of adult tickets sold was 88. Since the total number of tickets was 140, the number of senior tickets sold was 140−88=52.