Warm Up #1 #2 A chemist wants to create a 28% acid solution for an experiment by adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine? Jim says to Tina, if you give me $18, then Id have exactly five times as much money as you. Tina replies, Why thats not fair. I think you should give me $6 then wed have the same amount of money. How much money does Jim have to start with?

Warm Up #1 A chemist wants to create a 28% acid solution for an experiment by adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine? a a = amount of 100% acid b b = amount of 20% acid solution 0.28(20) = 5.6 Amount of Solution acid a b a 0.20b = 100% solution 20% solution 28% solution

Warm Up #1 A chemist wants to create a 28% acid solution for an experiment by adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine? a a = amount of 100% acid b b = amount of 20% acid solution

Warm Up #2 Jim says to Tina, if you give me $18, then Id have exactly five times as much money as you. Tina replies, Why thats not fair. I think you should give me $6, then wed have the same amount of money. How much money does Jim have to start with? J J = Jims money T = Tinas money Define variables: Write two equations E1 E2 First exchange Second exchange

Word Problems

#3 If you decrease the denominator of a fraction by four, the new fraction that is equal to 1/2. If you subtract one from the numerator of the original fraction, then the resulting fraction would be 1/3. What is the product of the original numerator and denominator? n n = Numerator d = Denominator Define variables: Write two equations E1 E2 Homework

#3 n n = Numerator d = Denominator Define variables: Write two equations Homework E1 E2 If you decrease the denominator of a fraction by four, the new fraction that is equal to 1/2. If you subtract one from the numerator of the original fraction, then the resulting fraction would be 1/3. What is the product of the original numerator and denominator?

Homework #6 Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today? B B = Beths age F = Franks age Define variables: Write two equations E1 E2 5 years ago Next year

Homework A rectangle has a perimeter of 18 inches. A new rectangle is formed by doubling the width and tripling the length. The new rectangle has a perimeter of 46 inches. Find the area of the new rectangle. L L = Length W = Width Define variables: Write two equations #7 E1 E2

#8 a a = amount of pure O.J. b b = amount of 32% O.J. 0.15(2) = 0.3 Amount of Solution O.J. a 2 b 1.00a b + = 100% solution 15% solution 32% solution Homework A two-gallon mixture of fruit juice is comprised 15% orange juice. Michelle wants a fruit juice mixture to be 32% orange juice. How much pure orange juice should she add to the mixture?

#8 A two-gallon mixture of fruit juice is comprised 15% orange juice. Michelle wants a fruit juice mixture to be 32% orange juice. How much pure orange juice should she add to the mixture? Homework a a = amount of 100% O.J. b b = amount of 32% O.J.

Word Problems

Word Problems

Homework Sadie works at the China Emporium packing dishes for shipments. She receives 12 cents for each piece she packs successfully and is fined 18 cents for each piece she breaks. If she handles 188 pieces and is paid $20.16, how many pieces does she break? p p = number packed b = number broken Define variables: Write two equations E1 E2 #1

Homework Traveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air. To Chicago With the wind To S.D. Against the wind w = speed of wind (to S.D.) p = speed of the plane #2

Homework #2 Traveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air. w = speed of wind (to S.D.) p = speed of the plane

Homework #3 One number is two-thirds of another number. If the larger number is increased by 9 it becomes twice as large as the smaller number. Find the product of the two numbers. L L = Larger number S = Smaller number Define variables: Write two equations E1 E2

Homework #4 A store received $823 from the sale of 5 iPods and 7 video games. The receipts from the iPods exceeded receipts from the video games by $137. What is the cost of a video game? p p = cost of an iPod v = cost of a video game Define variables: Write two equations E1 E2