Please help answer with steps thanks so much.

Question

The admission fee at an amusement park is $4.00 for children and $4.80 for adults. On a certain day, 344 people entered the park, and the admission fees collected totaled 1536 dollars. How many children and how many adults were admitted?

Answer 1

You need two answers, so you'll need two different equations.

Let A = the number of Adult tickets, and C the number of Children's tickets

 

You can write an equation that describes the total cost of tickets.

1) 4.80A + 4.00C = 1536

 

You can write another equation that describes the total number of tickets.

2) A + C = 344

 

To solve a system of equations, you first need to find a way to eliminate one of the variables to get a single equation with only one variable.  Substitution is often the easiest way to do this.

 

Solve equation 2 for one of the variables in terms of the other.  I'll solve for A.

A = 344-C

 

Substitute (344-C) for A in the other equation.

4.8(344-C) + 4C = 1536

1651.2 - 4.8C + 4C = 1536

115.2 = 0.8C

144 = C

 

Substitute 144 for C in either equation.  Pick the one that looks easier to work with.

A + 144 = 344

A = 200