math word problem

Question

The admission fee at an amusement park is $4.00 for children and $5.80 for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled 1313 dollars. How many children and how many adults were admitted?

Answer 1

Hi joe.

Let me chart the information given.

admission fee admission fee Total # admitted Total admission

per child per adult adult & children fee collected

$4.00- $5.80 281 $1313

To find the number of children and the number of adults admitted.

Approach

Step 1; Define suitable variables for the unknowns.

Let the number of children be c.

Let the number of adults be a.

Step2: Let us model the problem using 2 equations, because we have 2 unknowns.

c + a = 281 This is the equation for total number of adults and children admitted.

4.00c + 5.80a =$1313 This is the equation for the total admission fee collected.

Step 3: Solve

We have a system of equations. We can use the Substitution method or the Elimination by Addition method.

Let me guide you with the Elimination by Addition method. The goal is to eliminate a variable, and reduce the problem to a single equation. I plan to eliminate the variable c. As the method suggests that the elimination is by adding, here are the details of the plan.

Multiply the first equation by -4. The second equation is retained as it is. Then we add the modified 1st equation and the retained 2nd equation.

-4c-4a = -1124

+

4c +5.80a =1313

If it helps, feel free to re-write the 2 equations in the following order.

4c + 5.80a = 1313

+

-4c - 4,00a =-1124

-------------------------

1.80a = 189

Dividing both sides by 1.80,

a = 189/1,80

a = 105

Remember! a represents the number of adults,

Now we will use the equation c+a =313 and find the value of c.

c+105 = 313.

Subtract 105 from both the sides of the equation and we get c=313-105.

So, c= 208.

Answer: 208 children and 105 adults were admitted to the amusement park,

END OF PROBLEM.

I encourage you to try this problem using the Substitution Method and share your work.

2 cool methods to try if you wish! Use the method you like.