Solve Solve for m 4 3 6 Math

Solve: Solve for m: 4 3 +- 6

Math 8 H Problem Solving Day 4 Mixture & Work Rate Problems Algebra 1 Glencoe Mc. Graw-Hill Jo. Ann Evans

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!

The verbal model for today’s mixture problems will always be: cost • amount 1 st item + cost • amount 2 nd 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

cost • amount + cost • amount wild rice 225 ·x = white rice + Remember, x was the amount of wild rice. 2 -x is the amount of white rice. · 75 (2 – x) cost • amount rice mixture = 180 · 2 225 x + 150 – 75 x = 360 150 x + 150 = 360 150 x = 210 x = 1. 4 Solution: The mix will contain 1. 4 lbs. of wild rice and 0. 6 lbs. 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 cheap candy 135 ·x + · cost · amount = candy mix 105 (30 – x) = 117 135 x + 3150 – 105 x = 3510 30 x + 3150 = 3510 · 30 30 x = 360 x = 12 Solution: The mix will contain 18 lbs. of $1. 05 candy and 12 lbs. of $1. 35 candy.

“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

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 His work rate is of the job in an hour. 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 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? Rate • time = work done Erin: Niki: Erin’s work done + Niki’s work done = 1 job + = 1

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

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

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