Expressions and word problems

1. Factor the following expressions:

a.3a + 9b

b.ax + ay -az

c.4a + 8b + 12c

d.-2x -4y

e.5m - 15n

2.Evaluate the expressions when x=3 and y=8

a.x + 2y

b.-4(y - x)

c.x - y

d.2x + 3y

e.y - 2(x+y)

3.Find the cost per ounce of each of the following sets of products, and tell which one is the better buy for each pair. You must show your work for both parts.

a.6 ounce tube of toothpaste for 2.30 or a 12 ounce tube of toothpaste for 4.10.

b.4 ounce can of spray for 2.99 or a 6 ounce can of spray for 4.99.

c.20 ounce bottle of water for 1.19 or 32 ounce bottle of water for 1.99

4.You can buy one of the following cars. You want to base your decision on which car gets the best gas mileage. Calculate the mile per gallon rate for each of the following cars and tell which one gets the best gas mileage. Show all work.

a.Car A can travel 290 miles on 12 gallons of gas

b.Car B can travel 400 miles on 16 gallons of gas

c.Car C can travel 100 miles on 3 gallons of gas

d.Car D can go 400 miles on 16 gallons of gas

e.Car E can go 175 miles on 10 gallons of gas.

5.A cleaning solution is made by mixing 1/3 teaspoon baking soda, 2 tablespoon of dishwashing liquid and 2 cups lukewarm water.

a. How many mL of dishwashing liquid is that?

b. How many mL of baking soda is that?

c. How many mL of water is that?

6.A recipe calls for 800 mL of sour cream

a. How many cups is that?

b. How many teaspoons is that?

c. How many tablespoons is that?

7.A radio station sends out waves in all directions from a tower at the center of the circle of broadcast range.

a.If the broadcast range has a diameter of 196 miles, determine how large an area is reached. Use π = 3.14.

b.If the broadcast range increases to a diameter of 210 miles, what is the area reached?

c.If the broadcast range decreases to a diameter of 140 miles, what is the area reached?

8.The preferred seating area of a music theater has a base that measures 34 yd and a height of 39.6 yd. Find the area if the shape of the theater is

a.A triangle

b.A parallelogram

c.A rectangle

9.When 1200 people were asked how often they went out to dinner.

200 said never

410 said two to three times a month

340 said less than once a month

250 said once a week or more.

a.What percentage said two to three times a month?

b.What percentage said less than once a month?

c.What percentage said once a week or more?

Final answer rounded to nearest tenth.

10.The last seven computer games sold at the local electronics store cost $20, $34, $46, $34, $49, $34, $49. Find the

a.Mean
b.Median
c.Mode