Setting up system problems.

Things to look for

A. What are you trying to find and how many?

B. Total words (cost, total)

C. Comparison words (more, less, twice, times, half)

D. Option statements (option, choice, list)

The column on the left shows the steps used to solve a problem using a system of equations. Use the column on the left to answer each question in the column on the right.

A soccer league offers two options for membership plans. Option A includes an initial fee of $40 and costs $5 per game played. Option B costs $10 for each game played. After how

many games will the total cost of the two options be the same?

X

Y

8 games

Solving systems (word problems) Example

An apartment building contains 80 units. Some of these are 1-bedroom units renting for $425 per month and some are 2-bedroom units renting for $550 per month. When the building is entirely rented, the total monthly rental income is $38,375. How many apartments of each type are there?

x y

x + y = $425

$425

$425

$550 $550

$550 $550

80

425x + 550y = 38,375

Since there are a total of 80 apartments some are x some are y but they add to 80.

Since the x apartments sell for 425, 425x is the total $ for them. Since the y apartments sell for 550, 550y is the total $ for them. Therefore the equation for both sales together is…

Practice 3. Two angles are supplementary(add up to 180). One angle is 400 more than the other angle. What are the measures of the angles?

x0

y0

X 0 + 40

x+ y = 180y = x + 40

You and several other people are helping your aunt move. At lunch you volunteer to go out to buy sandwiches. You get 6 chicken and 6 beef for $30. For dinner you go to the same place and buy 4 chicken and 8 beef for $30.60. What was the price of each sandwich?

+ = $30

+ = $30.60

At a pizza shop, two small pizzas, a litter of soda, and a salad cost $14. One small pizza, a litter of soda, and three salads cost $15. Three small pizzas and a liter of soda cost $16. What is the cost of a small pizza, a litter of soda, and a salad?

2p + c + s = 14p + c + 3s = 153p + c = 16

The juice bar at a health club receives a delivery of juice at the beginning of each month. Over a month period, the health club received 1200 gallons of orange juice, 900 gallons of pineapple juice, and 1000 gallons of grapefruit juice. The table shows the composition of each juice delivery. How many gallons of juice did the health club receive in each delivery?

Juice 1st 2nd 3rd

Orange 70% 30% 30%

Pineapple 20% 30% 30%

Grapefruit 10% 20% 40%

.7x + .3y + .3z = 1200

.2x + .3y + .3z = 900

.1x + .2y + .4z = 1000

You try:

1.) Suppose 28 members of your class went on a rafting trip. Class members couldeither rent canoes for $16 each or rent kayaks for $19 each. The class spent atotal $469. How many people rented canoes and how many people rentedkayaks?

2.) The sum of three numbers is −2. The sum of three times the first number, twice the second number, and the third number is 9. The difference between the second number and half the third number is 10. Find the numbers.