Warm up Solve:. Lesson 2-2 Applications of Algebra Objective: To use algebra to solve word problems.
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Transcript of Warm up Solve:. Lesson 2-2 Applications of Algebra Objective: To use algebra to solve word problems.
![Page 1: Warm up Solve:. Lesson 2-2 Applications of Algebra Objective: To use algebra to solve word problems.](https://reader036.fdocuments.in/reader036/viewer/2022082516/56649cf55503460f949c4bf6/html5/thumbnails/1.jpg)
Warm up
• Solve:
xx
6
2
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Lesson 2-2 Applications of Algebra
Objective: To use algebra to solve word problems
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Problem Solving Steps
– 1. Read the problem carefully– 2. Define the variable– 3. Write the equation– 4. Solve the problem– 5. Check you work!
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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
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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?
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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
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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?
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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
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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)
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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?
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Distance Problems (Uniform Motion)
• Distance = Rate x Time (d=rt)• Are the distances equal?• Do they add together to a total?
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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?
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• 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)
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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?
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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?
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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?
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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
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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?
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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?