x415

Solve for m:

2x

124

5x212

3x2

12

2x

45x2

3x2

x6)5x2(3)x2(4

x615x6x8 x615x2 x2x2 x41544

Solve:

7n5n11

m

n11m7nm5

n11)7n5(m )7n5()7n5(

4 3 6

+-

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 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 1st

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 · amountexp. candy +

cost · amountcheap candy

= cost · amount candy mix

135

x + 105 (30 – x) 117 30· · ·=

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 it’s:

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

31

31

What part of the job could he complete in x hours?

work rate • time = work done

3x

x31

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?

hourperjobtheof31

What is Niki’s work rate? hourperjobtheof51

The women will work together for x hours.

What part of the job will each complete in x hours?

Rate • time = work done

Erin:3x

x31

Niki:5x

x51

Erin’s work done + Niki’s work done = 1 job

+ = 1

3x

5x

Solution:

87

1

15x

3x

Multiply by 15 to clear

the fractions.x x15 15 15(1)

3 5

5 3

15x3x5

15x8

815

x

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 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.

21

31

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: 2

xx

21

Corey:3x

x31

Charlotte’s wk. done + Corey’s wk. done = 1 job

+ = 1

2x

3x

It will take hours -or- 1 hour and 12 minutes.

13x

2x

51

1

Solution:

56

x

)1(63x

62x

6

6x2x3 6x5

3 2The time can be expressed as a mixed

number or in separate

units.