Solve for m: Solve:

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

Mixture Problems These problems are just like COIN/VALUE/TICKET problems that we have already solved. You have value of items (money times #)

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 = pounds of wild rice Let 2 – x = pounds of white rice 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

2.25 x (2 – x) = 1.80(2) 225x – 75x = x = x = 210 Val. of wild rice + Val. of white rice = Val. of 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

Value of $1.35 candy + Value of $1.05 candy = Value of mixture 135 x (30 – x) · · · = Solution: The mix will contain 18 lbs. of $1.05 candy and 12 lbs. of $1.35 candy. 135x – 105x = x = x = 360 x = 12

“Work Rate” Problems Instead now it’s: work rate  time = part of 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 = part of 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 = hours What is Erin’s work rate? What is Niki’s work rate?

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

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 = hours Charlotte’s work rate: of the job per hour. Corey’s 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? Charlotte’s part + Corey’s part = 1 job