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Warm Up

Warm Up. Solve:. 4. 3. 6. Solve for m:. + -. Math 8H. Problem Solving Day 4 Mixture & Work Rate Problems. Algebra 1 Glencoe McGraw-Hill JoAnn Evans. Mixture Problems.

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Warm Up

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  1. Warm Up Solve: 4 3 6 Solve for m: +-

  2. Math 8H Problem Solving Day 4 Mixture & Work Rate Problems Algebra 1 Glencoe McGraw-Hill JoAnn Evans

  3. Mixture Problems In mixture problems two or more items, which have different unit prices, are combined together to make a MIXTURE with a new unit price. Later in the year we’ll solve this type of problem with two variables and a system of equations, but for now………………… 1 variable and 1 equation!

  4. The verbal model for today’s mixture problems will always be: cost • amount1st item cost • amount2nd item cost • amountmixture + =

  5. A 2-pound box of rice that is a mixture of white rice and wild rice sells for $1.80 per lb. White rice by itself sells for $0.75 per lb. and wild rice alone sells for $2.25 per lb. How much of each type of rice was used to make the mixture? Let x = amt of wild rice in the mix Let 2 – x = amount of white rice in the mix Remember, the entire box is 2 pounds. If the wild rice (x) is removed from the box, what is left? Entire box – wild rice 2 - x white rice

  6. cost • amount + cost • amount = cost • amount wild rice white rice rice mixture · · · + = (2 – x) 75 225 x 180 2 225x + 150 – 75x = 360 Remember, x was the amount of wild rice. 2-x is the amount of white rice. 150x + 150 = 360 150x = 210 x = 1.4 Solution: The mix will contain 1.4 lbs. of wild rice and 0.6 lbs. of white rice.

  7. Candy worth $1.05 per lb. was mixed with candy worth $1.35 per lb. to produce a mixture worth $1.17 per lb. How many pounds of each kind of candy were used to make 30 lbs of the mixture? Let x = amt. of $1.35 candy in mix Let 30 – x = amt. of $1.05 candy in mix Let the more expensive item be “x”. There will be fewer negatives in the problem.

  8. cost · amount exp. candy cost · amount cheap candy cost · amount candy mix = + · · · = + (30 – x) x 135 105 117 30 135x + 3150 – 105x = 3510 30x + 3150 = 3510 30x = 360 x = 12 Solution: The mix will contain 18 lbs. of $1.05 candy and 12 lbs. of $1.35 candy.

  9. “Work Rate” Problems Work rate problems are similar to the problems we did using the formula rate  time = distance Instead now it’s: work rate  time = work done

  10. Work rate is the reciprocal of the time needed to complete the whole job. For example, if Andrew can complete a job in three hours………… he could complete of the job in an hour. His work rate is of the job per hour. work rate • time = work done

  11. What part of the job could he complete in x hours? work rate • time = work done

  12. Erin owns a florist shop. It takes her 3 hours to arrange the flowers needed for a wedding. Her new assistant Niki can do the same job in 5 hours. How long will it take the two women to complete the job together? Let x = amount of time to do the job together What is Erin’s work rate? What is Niki’s work rate?

  13. The women will work together for x hours. What part of the job will each complete in x hours? Rate • time = work done Erin: Niki: Erin’s work done + Niki’s work done = 1 job + = 1

  14. Multiply by 15 to clear the fractions. 5 3 Express time in the form of a mixed number. Solution: It will take hours to complete the job together.

  15. Charlotte and Corey share a car. Charlotte can wash and wax the car in two hours, but it takes Corey 3 hours to complete the same job. How long will it take them to wash and wax the car if they’re working together? Let x = amount of time to do the job together Charlotte’s work rate: of the job per hour. Corey’s work rate: of the job per hour.

  16. They will work together on the car for x hours. What part of the job could each complete alone in x hours? Rate • time = work done Charlotte: Corey: Charlotte’s wk. done + Corey’s wk. done = 1 job + = 1

  17. The time can be expressed as a mixed number or in separate units. 3 2 Solution: It will take hours -or- 1 hour and 12 minutes.

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