Question

A restaurant manager states the number of customers that enter the restaurant is equal to 4 times the number of people that buy a hotdog from the hotdog cart plus 9. The manager also states that the number of customers that enter their restaurant is equal to 3 times the number of people that buy a hotdog from the hotdog cart plus 35. What number of people buying a hotdog from the hotdog cart across the street makes the equation 4x+9=3x+35 true? Round your answer to the nearest whole number.

Answer 1

26 customers

Explanation:

Represent customers entering as y and those buying hot dogs as x

`y = 4x + 9`

`y = 3x + 35`

Required

Determine the number of people buying hotdogs (x)

Substitute 4x + 9 for y in the second equation

`4x + 9 = 3x + 35`

Collect Like Terms

`4x - 3x = 35 - 9`

`x = 26`