Question 1

Which of the following equations is an identity (true for all real numbers)?

Accepted Answer

$$2x + 3 = 2x + 3$$

Question 2

Solve the formula $$A = \frac{1}{2}bh$$ for $$b.$$

Accepted Answer

$$b = \frac{2A}{h}$$

Question 3

A store offers a 25% discount on a jacket, and the sale price is $90. What was the original price of the jacket?

Accepted Answer

$$120$$

Question 4

Given the formula $$P = 2l + 2w$$, solve for $$l in $$terms of $$P$$ and $$w.$$

Accepted Answer

$$l = \frac{P - 2w}{2}$$

Question 5

A sum of money is split into two accounts: one at 4% interest and the other at 6%. If $$2000 is $$invested at 4% and $$3000 at 6$$%, what is the total annual interest earned?

Accepted Answer

$$260$$

Question 6

A hotel room costs $$250$$ per night including a 10% tax. What is the price before tax?

Accepted Answer

$$227.27$$

Question 7

Solve for $$x$$: $$ac + b = 3(x - a).$$

Accepted Answer

$$x = \frac{ac + b}{3} + a$$

Question 8

A computer repair shop charges $$560$$ for a job, with $$80$$ for parts and the rest for labor at $$40$$ per hour. How many hours of labor were charged?

Accepted Answer

$$12$$

Question 9

You are comparing two gym memberships. Plan A charges a $$50$$ sign-up fee plus $$20$$ per month. Plan B charges a $$30$$ sign-up fee plus $$25$$ per month. After how many months will the total cost be the same?

Accepted Answer

$$4$$

Question 10

The perimeter of a rectangular garden is $$180$$ meters. The width is $$10$$ meters more than the length. What are the dimensions of the garden?

Accepted Answer

$$l = 40 m$$, $$w = 50 m$$

Question 11

Solve the formula $$V = \frac{1}{3}\pi r^2$ h$$ for $$h.$$

Accepted Answer

$$h = \frac{3V}{\pi r^2$}$$

Question 12

A rectangular swimming pool is twice as long as it is wide. If the perimeter is $$180$$ feet, what are the dimensions?

Accepted Answer

$$l = 60 ft$$, $$w = 30 ft$$

Question 13

Which of the following equations has no solution?

Accepted Answer

$$2x + 3 = 2x + 5$$

Question 14

A sum of money is invested in two accounts: one at 2% and another at 3%. The amount in the 3% account is $$2000$$ more than the amount in the 2% account. If the total annual interest is $$460$$, how much is invested at 2%?

Accepted Answer

$$6000$$

Question 15

Solve the formula $$A = \frac{1}{2}bh$$ for $$h.$$

Accepted Answer

$$h = \frac{2A}{b}$$

Question 16

After a 15% discount, a laptop costs $$850. $$What was the original price?

Accepted Answer

$$1000$$

Question 17

A rectangular field has a perimeter of $$300$$ meters. The length is $$20$$ meters less than twice the width. What are the dimensions?

Accepted Answer

$$l = 100 m$$, $$w = 60 m$$

Question 18

If $$D = rt$$, solve for $$t.$$

Accepted Answer

$$t = \frac{D}{r}$$

Question 19

You are choosing between two video streaming services. Company A charges a $$15$$ membership and $$5$$ per movie. Company B charges a $$25$$ membership and $$3$$ per movie. For how many movies will the total cost be the same?

Accepted Answer

$$5$$

Question 20

A sum of money is split into two accounts: one at 5% and the other at 7%. The amount in the 7% account is $$4000$$ more than the amount in the 5% account. If the total annual interest is $$820$$, how much is invested at 5%?

Accepted Answer

$$6000$$

Solving Linear Equations and Applications in College Algebra

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