The admission fee at a small fair is $1.50 for children, and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults entered?

Answer: 700 adults and 1500 children

Step-by-step explanation:

Let the number of adults be x and the number of children be y, then

x + y = 2200 ... equation 1

4x + 1.5y = 5050 ... equation 2

solving the system of linear equation by substitution method, from equation 1 make x the subject of the formula, that is

x = 2200 - y ... equation 3

substitute x = 2200 - y into equation 2, that is

4 (2200 - y) + 1.5y = 5050

8800 - 4y + 1.5y = 5050

8800 - 2.5y = 5050

2.5y = 8800 - 5050

2.5y = 3750

y = 3750/2.5

y = 1500

substitute y = 1500 into equation 3, we have

x = 2200 - y

x = 2200 - 1500

x = 700

Therefore, 700 adults and 1500 children entered