Solving Applied Problems: Two Equations? problem 1

The St.mark's Community bbq served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?

Question

The St.mark's Community bbq served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?

Hazel Anglin · Accepted Answer

Yes, you can build two equations here. #c# = amount of child's plates
#a# = amount of adult's plates What do you know?
1) you know that in total, 250 diners were served.
So, #c + a = 250# What else do you know?
2) The costs for each plates and the total cost. This can be expressed as the following equation:
#3.5 c + 7 a = 1347.5# Now, to solve the linear equation system, I would solve the first one for #c# or #a# - your choice - and plug it in the second. For example, you can solve the first equation for #c#: 
#c = 250 - a# Pluging this in the second equation gives you:
#3.5 * ( 250 - a) + 7 a = 1347.5#
#875 - 3.5 a + 7 a = 1347.5#
#3.5 a = 472.5#
#a = 135# This means that there were #135# adult's plates. The only thing left to do is to compute the amount of child's plates:
#c = 250 - a = 250 - 135 = 115# Result: #135# adult's plates, #115# child's plates.

Solving Applied Problems: Two Equations? problem 1 The St.mark's Community bbq served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?

The St.mark's Community bbq served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?