Solving real-world linear equations

Solving real-world linear equations

Multiple Choice

Do Now: 

 $Solve\ for\ y\$  

 $2y\ +\ 5\ =\ 25$  

•  $y\ =\ 15$  

•  $y\ =\ 10$  

•  $y\ =\ 7.5$  

•  $y\ =\ 60$  

Multiple Choice

 $\frac{-12}{k\ }\ =\ 6$                           Solve for k

•  $k\ =\ 72$  

•  $k\ =\ 2$  

•  $k\ =\ -2$  

•  $k\ =\ -18$  

How can we translate a word problem into an algebraic equation?

• Read the problem more than once.

• Write down the missing information that you are trying to solve for i.e. price of a shirt, price of a sandwich, length of a fence, balance in your account etc. Each of these real-world concepts can be represented by a variable.

• Write a let statement...let b represent the missing balance, let p represent price etc.

• Look for keywords such as more than (add), less than (subtract), twice as many (x2), half as much (/2), etc. These phrases will help you write the appropriate linear equation.

• Solve and check. Make sure your answer makes sense in the context of the problem. If you get negative sandwiches you probably didn't write the correct equation.

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The balance of an investment account is $308 more than the balance 4 years ago. The current balance of the account is $4708. What was the balance 4 years ago?

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A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car.

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A discounted amusement park ticket costs $12.95 less than the original price p. The discounted ticket costs $44. Write and solve an equation to find the original price.

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During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours must you work as a landscaper?

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You order two tacos and a salad. The salad costs $2.50. You pay 8% sales tax and leave a $3 tip. You pay a total of $13.80. How much does one taco cost?