College Algebra Word Question Function

Question

The Downtown Community Barbecue served 372 dinners. A child’s plate cost $3.50 and an adult’s plate cost $9.00. A total of $2,121.50 was collected. How many of each type of plate was served?

Round answers to the nearest whole person.

child plates were served.

 adult plates were served.

Answer 1

You can solve this problem by creating two equations with two unknowns and solving them.

Let's use the variable, c, to represent the NUMBER of child plates and the variable, a, to represent the NUMBER of adult plates.

Since there are a total of 372 dinners, we can write the following equation:

c + a = 372

Then since each child plate was $3.50 and each adult plate was $9 with a total of $2121.50 collected, we can write the following equation:

3.50c + 9a = 2121.50

Now solve these two equations using elimination. Multiply the first equation by -9 and solve for c:

-9c - 9a = -3348

3.50c + 9a = 2121.50

-5.50c = -1226.50

c = 223

There were 223 child plates.

Since there were a total of 372 plates, there will be 149 adult plates (223 + 149 = 372)

To verify, the total amount raised would be $2121.50:

3.50c + 9a = 2121.50

3.50*223 + 9*149 = 780.50 + 1341.00= $2121.50