# Intermediate Algebra Problems With Answers - Sample 3

A set of intermediate algebra problems, with answers, are presented. The solutions are at the bottom of the page.

1. Solve the follwoing system of equations

-x/2 + y/3 = 0

x + 6y = 16

2. How many real solutions does each quadratic equation shown below have?

a) x 2 + (4 / 5) x = - 1/4

b) x 2 - 7x + 10 = 0

c) x 2 - (2/3) x + 1/9= 0

3. Does the data in the table below represents y as a function of x? Explain.

x y
1 - 10 4
11 - 20 6
21 - 30 8
30 - 40 12
40 - 50 16
51 - 60 34

4. Solve the following quadratic equation.

0.01 x 2 - 0.1 x - 0.3 = 0

5. In a cafeteria, 3 coffees and 4 donuts cost \$10.05. In the same cafeteria, 5 coffees and 7 donuts cost \$17.15 Dirhams. How much do you have to pay for 4 coffees and 6 donuts?

6. Find the slope of the lines through the given points and state whether each line is vertical, horizontal or neither.

Line L1 : (-2 , 3) and (8 , 3)

Line L2 : (4 , 3) and (4 , -3)

Line L3 : (-1 , 7) and (3 , -3)

7. Find four consecutive even integer numbers whose sum is 388.

8. Going for a long trip, Thomas drove for 2 hours and had lunch. After lunch he drove for 3 more hours at a speed that is 20 km/hour more than before lunch. The total trip was 460 km.

a) What was his speed after lunch?

9. Compare the following expressions: a) 2 -4 , b) (-2) -4 , c) (-1/2) 4

10. Evaluate and convert to scientific notation.

(3.4 × 10 11)(5.4 × 10 -3)