While working with the word problems for this section, it is a good idea to help organize your thoughts using the following steps. In a testing situtation I would need to see at least steps 1 -3 below. Take a look at the example below and use the steps provided to work through all the word problems of this section.

Example: The admission fee at an amusement park is $5 for children and $9 for adults. ON a certain day, 450 people enter the park and the admission fees collected totaled $3050. How many children and how many adults were admitted?

1) First step, identify variables with what you are trying to find.

In the last sentence it says 'How many children and how many adults were admitted?' So our 2 'unknowns' are number of children and number of adult admitted

Let C = number of children admitted in the park
Let A = number of adults admitted in the park

Identifying your variables should be written out on your paper (i.e. if in a testing situation, I would need to see that you identified your unknowns)

2) Second step is to build the equations to represent the situation.

In the first sentence we were told that 'The admission fee at an amusement park is $5 for children and $9 for adults' and we also know that the fees for the day totaled $3050. We can translate these facts to a mathematical equation as

5.00C + 9.00A = 3050

This equation represents the amount of money made in admission fees for the day. ($5 for each children ticket, which we don't know the amount yet, so we use C as identified above, and $9 for each adult ticket sold, A, to give a total of $3050 in admission sales)

We can build another equation knowing that a total of '450 people entered the park on this certain day'. We don't know the amount of children and adults that entered, however since we have identified them as our unknowns, C and A, we can represent this phrase as

C + A = 450.

This equation represents the total number of people who entered the park.

We now have a system of 2 equations with 2 unknowns.

5.00C + 9.00A = 3050
C + A = 450.

3) Solve the system.

You can solve using any method (substitution or elimination). Here I will solve using the substitution method

5.00C + 9.00A = 3050 (1)
C + A = 450. (2)

From equation (2), C = 450 -A

Substitute this expression for C in equation (1), and solve for A

5.00(450-A) + 9.00A = 3050

2250 - 5.00A + 9.00A = 3050

4.00A = 800

A = 200

Substitute A = 200 into equation (1) or (2) and solve for C

C + 200 = 450

C = 250

Thus the number of children tickets sold was 250 and number of adult tickets was 200.

4) CHECK your WORK!

You can always make sure that you have the correct answer by checking your work. Substitute in A = 200 and C = 250 into BOTH equations 1 and 2.

5.00(250) + 9.00(200) = 1250 + 2250 = 3050

and for equation (2)

250 + 200 = 450