Algebra 1 Glencoe McGraw-Hill JoAnn Evans

Mixed Problem Solving

Practice

Two cars, 700 miles apart, decide to travel until they meet. One leaves 4 hours ahead and travels at 30 mph. The other leaves going 50 mph. How long after the second car leaves will the two cars

meet?

Let x = 2nd car’s time

Let x + 4 = 1st car’s time

distance of 1st car + distance of 2nd car = total distance

30(x + 4) + 50x = 700

30x + 120 + 50x = 700

80x = 580

x = 7.25

They’ll meet 7.25 hours after the second car leaves.

700 miles

1st 2nd

Alicia has 8 more nickels than quarters. The total value of her coins is $3.70. How many

of each coin does she have?

Let x = # quarters

Let x + 8 = # nickels

value of quarters + value of nickels = total

25x + 5(x + 8) = 370

25x + 5x + 40 = 370

30x = 330

x = 11

Alicia has 11 quarters and 19 nickels.

Let 25x = value of quarters

Let 5(x + 8) = value of nickels

Bob can paint a small house in 20 hours. Ray could paint the same house in 16 hours. How long would the job take if Bob and Ray worked

together?Let x = time to do the job together

1Bob's work rate is of the job per hour.

201

Ray's work rate is of the job per hour.16

Bob’s work done + Ray’s work done = 1 house painted

1x

20

x16

x x80 80 80 1

20 16

4 5

x x1

20 16

4x 5x 80

9x 80

80x

9

8x 8 hours

9

8Bob and Ray can paint the house in 8 hours.

9

Hector built a rectangular fish pond that is surrounded by a brick sidewalk that’s 2 meters

wide. The area of the sidewalk is 76 m2. Find the dimensions of the pond if it is twice as long as it is

wide.Let x = pond width

Let 2x = pond length2x

x

2 + 2x+ 2

2 +

x +

2

Let x + 4 = total width

Let 2x + 4 = total length

area of pond + area of brick walk = total area

2x(x) + 76 = (2x + 4)(x + 4) 2x2 + 76 = 2x2 + 8x + 4x +

16 76 = 12x + 16

60 = 12x5 = x

The pond is 5 meters by 10

meters.

The length of a rectangle is 4 more than its width. The perimeter of the rectangle is 34 more than twice the length. Find the dimensions of the

rectangle.

Let w = width

Let w + 4 = length

Perimeter = two times the length + 34

2w + 2(w + 4) = 2(w + 4) + 34

2w + 2w + 8 = 2w + 8 + 34

4w + 8 = 2w + 42

2w = 34The rectangle is 17 units by

21 units.

w + 4

w

w = 17

The snack mix will contain 9 lbs. of M&Ms and 6 lbs. of peanuts.

· · ·200

x + 150 (15 – x) = 180 15

200x + 2250 – 150x = 2700

50x + 2250 = 2700

50x = 450

x = 9

cost • amount + cost • amount = cost • amount M&Ms peanuts snack mix

M&Ms selling for $2/lb are mixed with peanuts selling for $1.50/lb to make 15 lbs. snack mix that will sell for $1.80/lb. How many pounds of M&Ms

and how many pounds of peanuts are contained in the mix?

Let x = # lbs. of M&Ms

Let 15 - x = # lbs. of peanuts