Kaivon D.

asked • 12/03/19# At an all you can eat barbecue fundraiser that you are sponsoring ,adults pay $6 for a dinner and children pay $4 for a dinner. 212 people attend and you raise $1128.

What is the total number of adults and the total number of children?

a. What is a system of equations that you can use to solve this problem?

b. What method would you use to solve this system?

## 1 Expert Answer

Paige N. answered • 12/03/19

Math/Science/AutoCad tutor specializing in SAT, Regents, K-12 testing

Let's set up 2 equations: one for the total number of people attending and one for the amount of money raised.

Adults = a Children = c

The number of people attending would be: a+c = 212

The amount of money raised would be: 6a +4c = 1,128

You can solve this problem by using the substitution method or the elimination method. Let's use the elimination method and get rid of variable a.

By multiplying the top equation by -6, we can cancel out variable a.

-6a-6c = -1,272

6a+4c = 1,128

Now add the two equations together.

-2c = -144 c= 72

Now substitute C back into one of your original equations.

a+c=212

a+72=212

a = 140

So there are 72 children and 140 adults attending.

To check your work, substitute both of your found values into the second equation.

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Paige N.

Let's set up 2 equations: one for the total number of people attending and one for the amount of money raised. Adults = a Children = c The number of people attending would be: a+c = 212 The amount of money raised would be: 6a +4c = 1,128 You can solve this problem by using the substitution method or the elimination method. Let's use the elimination method and get rid of variable a. By multiplying the top equation by -6, we can cancel out variable a. -6a-6c = -1,272 6a+4c = 1,128 Now add the two equations together. -2c = -144 c= 72 Now substitute C back into one of your original equations. a+c=212 a+72=212 a = 140 So there are 72 children and 140 adults attending. To check your work, substitute both of your found values into the second equation.12/03/19