Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H Problem Solving Day 4 Mixture & Work Rate Problems
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 well solve this type of problem with two variables and a system of equations, but for now………………… 1 variable and 1 equation!
The verbal model for todays mixture problems will always be: cost amount 1 st item cost amount 2nd item cost amount mixture +=
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
Solution: The mix will contain 1.4 lbs. of wild rice and 0.6 lbs. of white rice. 225 · x + 75 · (2 – x) = 180 · 2 225x + 150 – 75x = 360 150x + 150 = 360 150x = 210 x = 1.4 cost amount + cost amount = cost amount wild rice white rice rice mixture Remember, x was the amount of wild rice. 2-x is the amount of white rice.
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.
cost · amount exp. candy + cost · amount cheap candy = cost · amount candy mix 135 x + 105 (30 – x) 11730 · · · = Solution: The mix will contain 18 lbs. of $1.05 candy and 12 lbs. of $1.35 candy. 135x + 3150 – 105x = 3510 30x + 3150 = 3510 30x = 360 x = 12
Work Rate Problems Instead now its: work rate time = work done Work rate problems are similar to the problems we did using the formula rate time = distance
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
What part of the job could he complete in x hours? work rate time = work done
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 Erins work rate? What is Nikis work rate?
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: Erins work done + Nikis work done = 1 job + = 1
Solution : Multiply by 15 to clear the fractions. 53 It will take hours to complete the job together. Express time in the form of a mixed number.
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 theyre working together? Let x = amount of time to do the job together Charlottes work rate: of the job per hour. Coreys work rate: of the job per hour.
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: Charlottes wk. done + Coreys wk. done = 1 job + = 1
It will take hours -or- 1 hour and 12 minutes. Solution: 3 2 The time can be expressed as a mixed number or in separate units.