Warm up

• Solve:

xx

6

2

11

3

Lesson 2-2 Applications of Algebra

Objective: To use algebra to solve word problems

Problem Solving Steps

– 1. Read the problem carefully– 2. Define the variable– 3. Write the equation– 4. Solve the problem– 5. Check you work!

Single Variable Problems

• Prices & Discounts– If you pay $50 for a pair of shoes after receiving a

20% discount, what was the price of the shoes before the discount?

• Let s – price of shoes before discount• Discount = .20s• s - .20s = 50

Prices and Discounts• If you pay $75 for a new phone after receiving a

discount, and the original price was $125. How much discount did you receive?

Coin Problems• Carrie has 40 more nickels than Joan has dimes.

They both have the same amount of money. How many coins does each girl have?

• Let x = the number of coins that Joan has.

• 5(40 + x) = 10x• 200 + 5x = 10x• 200 = 5x• 40 = x

# of coins Value per coin

Total Value

Carrie 40 + x 5 5(40 + x)

Joan x 10 10x

Coin Problems

• Karl has some nickels and pennies totaling $1.80. He has 4 fewer pennies than three times the number of nickels. How many of each does he have?

Simple Interest

• Interest (I) = Principal(P) x rate(R) x time(t)• Principal= amount borrowed or invested• Total amount owed:

S = P + I = P + Prt

Simple Interest• A part of $10,000 was borrowed at 3% simple

annual interest and the remainder at 5%. If the total amount of interest due after 3 years is $1275, how much was borrowed at each rate?

P x r x t = Interest

3% s 0.03 3 0.09s

5% 10000-s 0.05 3 0.15(10000-s)

1275 = 0.09s + 0.15(10000-s)

Simple Interest• A part of $25,000 was borrowed at 7% simple

annual interest and the remainder at 4%. If the total amount of interest due after 4 years is $5000, how much was borrowed at each rate?

Distance Problems (Uniform Motion)

• Distance = Rate x Time (d=rt)• Are the distances equal?• Do they add together to a total?

Distance Problems (Uniform Motion)• Mary & Michael leave school traveling in

opposite directions. Michael is walking and Mary is biking, averaging 6 km/h more than Michael. If they are 18 km apart after 1.5 h, what is the rate of each?

• Andrew begins biking south at 20 km/h at noon. Justin leaves from the same point 15 min. later to catch up with him. If Justin bikes at 24 km./h, how long will it take him to catch up to Andrew?

Distance Problems (Uniform Motion)

Warm up

• Erin drove her car to the garage at 48 km/ h and then walked back home at 8 km/h. The drive took 10 min less than the walk home. How far did Erin walk and for how long?

Mixture Problems• A grocer makes a natural breakfast cereal by

mixing oat cereal costing $2 per kilogram with dried fruits costing $9 per kilogram. How many kilograms of each are needed to make 60 kg of cereal costing $3.75 per kilogram?

Mixture Problems• How many liters of water must be added to

20L of a 24% acid solution to make a solution that is 8% acid?

Work Problems• Involves 2 or more people or machines

completing a task.• The rate of work per unit of time is usually a

fraction. (If it takes 3 hour for it to complete the job the rate is 1/3 of a job per hour)

• Rate = job

• Work done = (Rate)(Time)

n

1

Work Problems• One printing press can finish a job in 8 h. The

same job would take a second press 12 h. How long would it take both presses together?

Work Problems• A mail handler needs 3 h to sort an average

day’s mail, but with an assistant it takes 2h. How long would it take the assistant to sort the mail working alone?