its on my homeworks

Question

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 264 people entered the park, and the admission fees collected totaled $746. Let  be the number of children that were admitted and let  be the number of adults that were admitted.Find an equation for total number of people that were admitted to the amusement park:  

  Find an equation for the total amount of adminssion fees that were collected:  

  Use those equations to find the following.

Find the total number of children that were admitted:    

Find the total number of adults that were admitted:    

Answer 1

140 Adult

124 Children

A system of equations in two unknowns, x and y should work here

x = children

y = adults

Equation 1 Total number of people admitted

x + y = 264

Equation 2 Total amount of admission fees collected

1.5x + 4y = 746

Use Equation 1 to set up a substitution

x + y = 264

y = 264 - x

Substitute this quantity for y in Equation 2

1.5x + 4(264 -x) = 746

1.5x + 1056 -4x = 746

Combine like terms

-2.5x + 1056 = 746

Subtract 1056 from both sides of the equation

-2.5x = -310

Divide both sides of the equation by negative 2.5

x = 124 children

y = 264 -x

y= 264 -124

y=140 adults

Checking in Equation 2

1.5(124) + 4(140) = 746

186 + 560 = 746

I hope you find this useful