Question

. An amusement park bought some arcade games that cost $2,000 each and photo booths that cost $3,200 each. A total of 22 of both types of machines were bought, for $53,600. How many arcade game machines did the park buy ?

Answer 1

14 arcade games and 8 photobooths were purchased

Explanation:

x will represent the number of arcade games

y will represent the number of photobooths

We know that 22 total machines were bought which means that x+y=22

We also know that the total was 53600 which means that 2000x+3200y=53600

We can use substitution to solve this

x+y=22

x-22= -y

-x+22=y

Then plug this in for y in the next equation

2000x+3200(-x+22)=53600

Solve this and get x=14

Then plug in x=14 into any equation (I will choose the x+y one because that's easiest to solve)

14+y=22

this means y=8

This means that 14 arcade games and 8 photobooths were purchased

I double checked the math on desmos and it is correct