Write a short story that contains a situation that can be represented by a system of equations with two variables and two equations. Show all work to solve the system, using all three methods. Include an explanation of the solution as it relates to the story.

A story that could fit in is;

Suppose the admission fee at a large fair is $1.50 for women and $4.00 for men. On a certain day, 2200 people enter the fair and $5050 is collected. How many women and how many men attended the large fair?

Using a system of equations we draft out variables;

number of men = m

number of women = w

Remember, from the question the total attended is:

total number: m + w = 2200 (equation 1)

total income: 4m + 1.5w = 5050 (equation 2)

Step 1

Solve the first equation for one of the variables, and then

Step 2

Substitute the result into (equation 2).

Step 1:

m = 2200 - w

4 (2200 - w) + 1.5w = 5050

8800 - 4w + 1.5w = 5050

8800 - 2.5w = 5050

-2.5w = - 3750

w = 1500

Step 2:

m = 2200 - (1500) = 700

Therefore,

attendance for men = 700

attendance for women = 1500