Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–7) CCSS Then/Now New Vocabulary Example 1:Solve for a Specific Variable Example 2: Solve for.

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Splash Screen

Lesson Menu Five-Minute Check (over Lesson 2–7) CCSS Then/Now New Vocabulary Example 1:Solve for a Specific Variable Example 2: Solve for a Specific Variable Example 3:Real-World Example: Use Literal Equations Example 4:Use Dimensional Analysis

Over Lesson 2–7 5-Minute Check 1 A.increase; 22% B.increase; 14% C.decrease; 14% D.decrease; 22% State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Round to the nearest whole percent. original: 84 new: 96

Over Lesson 2–7 5-Minute Check 2 A.increase; 5% B.decrease; 50% C.decrease; 58% D.decrease; 62% State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Round to the nearest whole percent. original: 47 new: 18

Over Lesson 2–7 5-Minute Check 3 A.$78.60 B.$75.65 C.$74.00 D.$67.53 What is the discounted price of a tent with a price of $89 and a discount of 15%?

Over Lesson 2–7 5-Minute Check 4 A.$62.44 B.$68.00 C.$74.41 D.$76.32 What is the final price of a pair of hiking boots with a price of $78, a discount of 10%, and a tax of 6%?

Over Lesson 2–7 5-Minute Check 5 A.5% increase B.7% increase C.12% increase D.5% decrease On July 1, a stock sold for $46 per share, and on August 1, it sold for $48.30 per share. What was the percent of change in the price of the stock?

Over Lesson 2–7 5-Minute Check 6 A.32% decrease B.36% increase C.39% decrease D.40% increase Olivia’s cell phone bill last month was $125. This month her bill is $85. What is the percent of change?

CCSS Pg. 126 – 131 Obj: Learn how to solve equations for given variables and use formulas to solve real-world problems. Content Standards: A.CED.4 and A.REI.3

Why? –Each year, more people use credit cards to make everyday purchases. If the entire balance is not paid by the due date, compound interest is applied. The formula for computing the balance of an account with compound interest added annually is A = the amount of money in the account including interest P = principal – the amount of money in the account before interest r = the interest rate written as a decimal t = time in years

In the formula, what operation do you perform to find A? Suppose you know the quantities for A and r, but not P. How would you solve for P? Why solve a formula for a specific variable before you substitute quantities for the know variables?

Then/Now You solved equations with variables on each side. Solve equations for given variables. Use formulas to solve real-world problems.

Vocabulary Literal Equation – an equation that involves several variables Dimensional Analysis or Unit Analysis – the process of carrying units throughout a computation

Example 1 Solve for a Specific Variable Solve 5b + 12c = 9 for b. 5b + 12c = 9Original equation 5b + 12c – 12c = 9 – 12cSubtract 12c from each side. 5b = 9 – 12cSimplify. Divide each side by 5. Simplify.

Example 1 Solve for a Specific Variable

Example 1 Solve 2x – 17y = 13 for y. A. B. C. D.y = 2x + 4

Example 2 Solve for a Specific Variable Solve 7x – 2z = 4 – xy for x. 7x – 2z = 4 – xyOriginal equation 7x – 2z + xy = 4 – xy + xyAdd xy to each side. 7x – 2z + xy = 4Simplify. 7x – 2z + xy +2z = 4 + 2zAdd 2z to each side. 7x + xy = 4 + 2zSimplify. x(7 + y) = 4 + 2zUse the Distributive Property.

Example 2 Solve for a Specific Variable Divide each side by 7 + y. Simplify.

Example 2 Solve 12a + 3c = 2ab + 6 for a. A. B. C. D. ; b ≠ 6 ; b ≠ –6 ; b ≠ 6

Example 3A Use Literal Equations Answer: Eg = m or m = Eg A. FUEL ECONOMY A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for m. Formula for fuel economy Multiply each side by g.

Example 3B B. FUEL ECONOMY If Quanah’s car has an average fuel consumption of 30 miles per gallon and she used 9.5 gallons, how far did she drive? Eg =mFormula for miles driven 30(9.5) =mE = 30 mpg and g = 9.5 gallons 285 =m Multiply. Answer: She drove 285 miles. Use Literal Equations

A. g = mE B. m = gE C.D. Example 3A A. FUEL ECONOMY A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for g.

Example 3B A.19 gallons B.1477 gallons C gallons D.80 gallons B. If Quanah drove 1477 miles and her pickup has an average fuel consumption of 19 miles per gallon, about how many gallons of fuel did she use?

Example 4 Use Dimensional Analysis CHIMPANZEES The average weight of the chimpanzees at a zoo is 52 kilograms. If 1 gram ≈ ounce, use dimensional analysis to find the average weight of a chimpanzee in pounds. (Hint: 1 lb = 16 oz) weight of chimpanzee kilograms to grams grams to ounces ounces to pounds 52 kg × × ×

52 kg × × ×= Example 4 Use Dimensional Analysis Notice how the units cancel, leaving the unit to which you are converting. Answer: The average weight of a chimpanzee is about 115 pounds.

Example 4 A.about 4.35 mi B.about 7 mi C.about 7.7 mi D.about 8 mi CHARITY Janet is walking 20 laps of a track in a relay to raise money for cancer research. If each lap is 350 meters, how many miles will Janet walk? (Hint: 1 meter  yards and 1 mile = 1760 yards)

End of the Lesson