Ratios and Percentages — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Use ratios or percentages to find the requested value.

   $$10\%\text{ of }50$$

   Answer: $5$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=5$$
2. 2.

   Use ratios or percentages to find the requested value.

   $$25\%\text{ of }80$$

   Answer: $20$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=20$$
3. 3.

   Use ratios or percentages to find the requested value.

   $$2:3,\text{total}=25,\text{first part}=?$$

   Answer: $10$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=10$$
4. 4.

   Use ratios or percentages to find the requested value.

   $$\frac{3}{5}=?\%$$

   Answer: $60$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=60$$
5. 5.

   Use ratios or percentages to find the requested value.

   $$40\text{ increased by }15\%$$

   Answer: $46$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=46$$
6. 6.

   Use ratios or percentages to find the requested value.

   $$120\text{ discounted by }25\%$$

   Answer: $90$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=90$$
7. 7.

   Use ratios or percentages to find the requested value.

   $$20\%\text{ of }60$$

   Answer: $12$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=12$$
8. 8.

   Use ratios or percentages to find the requested value.

   $$50\%\text{ of }90$$

   Answer: $45$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=45$$
9. 9.

   Use ratios or percentages to find the requested value.

   $$3:2,\text{total}=40,\text{first part}=?$$

   Answer: $24$

   Step-by-step solution

   1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
   2. $$\text{Find the part, then check it against the whole.}$$
   3. $$=24$$
10. 10.

    Use ratios or percentages to find the requested value.

    $$\frac{7}{10}=?\%$$

    Answer: $70$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=70$$
11. 11.

    Use ratios or percentages to find the requested value.

    $$80\text{ increased by }25\%$$

    Answer: $100$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=100$$
12. 12.

    Use ratios or percentages to find the requested value.

    $$200\text{ discounted by }10\%$$

    Answer: $180$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=180$$
13. 13.

    Use ratios or percentages to find the requested value.

    $$5\%\text{ of }300$$

    Answer: $15$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=15$$
14. 14.

    Use ratios or percentages to find the requested value.

    $$1:4,\text{total}=35,\text{first part}=?$$

    Answer: $7$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=7$$
15. 15.

    Use ratios or percentages to find the requested value.

    $$\frac{1}{8}=?\%$$

    Answer: $12$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=12.5$$
16. 16.

    Use ratios or percentages to find the requested value.

    $$60\text{ increased by }50\%$$

    Answer: $90$

    Step-by-step solution

    1. $$\text{Translate a percent into a fraction out of 100 or a decimal.}$$
    2. $$\text{Find the part, then check it against the whole.}$$
    3. $$=90$$

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• Order of Operations
• Signed Numbers
• Fraction Sense
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics