Lesson 7

Revisit Percentages

Let's use equations to find percentages.

Problem 1

A crew has paved \(\frac{3}{4}\) of a mile of road. If they have completed 50% of the work, how long is the road they are paving?

Problem 2

40% of \(x\) is 35.

  1. Write an equation that shows the relationship of 40%, \(x\), and 35.
  2. Use your equation to find \(x\). Show your reasoning.

Problem 3

Priya has completed 9 exam questions. This is 60% of the questions on the exam.

  1. Write an equation representing this situation. Explain the meaning of any variables you use.

  2. How many questions are on the exam? Show your reasoning.

Problem 4

Answer each question. Show your reasoning.

20% of \(a\) is 11. What is \(a\)?

75% of \(b\) is 12. What is \(b\)?

80% of \(c\) is 20. What is \(c\)?

200% of \(d\) is 18. What is \(d\)?

Problem 5

For the equation \(2n - 3 = 7\)

  1. What is the variable?
  2. What is the coefficient of the variable?
  3. Which of these is the solution to the equation? 2, 3, 5, 7, \(n\)
(From Unit 6, Lesson 2.)

Problem 6

Which of these is a solution to the equation \(\frac{1}{8}=\frac{2}{5} \boldcdot x\)?

A:

\(\frac{2}{40}\)

B:

\(\frac{5}{16}\)

C:

\(\frac{11}{40}\)

D:

\(\frac{17}{40}\)

(From Unit 6, Lesson 2.)

Problem 7

Find the quotients.

  1. \(0.009 \div 0.001\)

  2. \(0.009 \div 0.002\)

  3. \(0.0045 \div 0.001\)

  4. \(0.0045 \div 0.002\)
(From Unit 5, Lesson 13.)