You have been practising three types of percent problems. You have learned that one proportion can be used to solve all the problems:

[latex]\dfrac{\text{is (part)}}{\text{of (whole)}}=\dfrac{\%}{100}[/latex]

1. Finding a Percent of a Number
   • You are given the percent and the whole.
   • The missing term is the part (call it N). [latex]\dfrac{\textit{N}}{\text{whole}}=\dfrac{\%}{100}[/latex]
2. Finding What Percent One Number is of Another
   • You are told the part and the whole.
   • The missing term is the percent (call it P). [latex]\dfrac{\text{part}}{\text{whole}}=\dfrac{\textit{P}}{100}[/latex]
3. Finding a Number When a Percent of it is Given
   • You are given the part and the percent.
   • The missing term is the whole (call it W). [latex]\dfrac{\text{part}}{\textit{W}}=\dfrac{\%}{100}[/latex]

Real-life situations and real math problems often require several steps to collect and organize all the information. Look for those extra steps in the problems that follow.

When you read the problems, look for the part, the whole and the percent. Decide which term is missing. Once you know which term is missing, the problem can be solved by using the proportion [latex]\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}[/latex] or the appropriate short method.

More Working With Percent Review

Solve these problems using proportion. Write all your work with the problem so your instructor can help you should you have any difficulty. Remember to check that the answer makes sense and to write a sentence answer. For these problems, round your answers this way:

• Percents to the nearest tenth of a percent
• Money to the nearest cent
• Decimal fractions to the nearest thousandth

1. You need a minimum of 80% on the test, which means you must get at least 36 marks. What are the total possible marks on the test?
2. Ann and Joe bought their home twelve years ago and have paid 45% of the principal amount of their mortgage. They have paid $18000 towards the principal of the mortgage. What was the principal amount of the mortgage to start with?
3. The waiters at the restaurant must contribute money to be shared among the cocktail servers and kitchen staff. Each waiter contributes 4% of his or her total food and drink sales. Craig’s total sales were $645 in his 5-hour shift.
   1. How much money must he contribute to the kitchen and cocktail servers?
   2. Craig made 12% in tips on his sales tonight. What amount were his tips?

    

4. The cost of hydroelectric power for our home last year was 210% of what it was six years ago. Last year, our power bill totalled $960. How much was it six years ago?
5. 16⅔% of the tickets for the rock concert were sold in the first hour the telephone order lines were open. In that hour, 2500 tickets were sold. What was the total number of tickets available for the concert?
6. The total student enrolment in the school district has increased from 18506 to 19724 students in the last year. What is the percent of this increase in student enrolment?
7. Al bought his secondhand off-road motorcycle for $1500 and sold it three years later for $1175. By what percent did his motorcycle depreciate (decrease in value)?
8. Pat operates a street vendor’s cart selling hot dogs, sausages on a bun and soft drinks. The basic pay is $100 per week with a 28% commission on all sales over $450 in a week. Pat sold $1244 of food and soft drinks last week. Calculate Pat’s earnings from the street-vending cart for the week.
9. The 1500 blouses purchased by the large retail chain of ladies’ clothing stores cost the company a total of $24000. The blouses were then priced to sell at $45 each. What is the percent of the mark-up on these blouses?
   (Hint: First, calculate the company’s cost price for each blouse.)
10. Maureen was happy to see that she got 27 out of 30 on her English essay. What percent did she get?
11. The ski jackets were on the summer clearance rack marked “45% off”.
    1. What is the sale price of a jacket priced regularly at $229.95?
    2. What is the total cost of this jacket with H.S.T (12%)?

     

12. Tuition fees at the university have increased from $49 per credit hour to $62 per credit hour in the last three years. What is the percent of the tuition increase?
13. Jill bought 3 bottles of liquor in the US. The bill, including US sales tax, was $28.50. Assume the American dollar was $1.08 Canadian. Calculate:
    1. the value of the liquor in Canadian funds.
    2. duty at 110%.
    3. HST at 12% (on Canadian value + duty).
    4. total cost in Canadian funds.

     

14. The consignment store will sell your good used women’s clothing for you. The store owners take a percentage of the selling price as their fee for service. The consignment charges (the % the store owners keep) are as follows:
    [latex]\begin{equation}\begin{split} &\text{Coats} &\hspace{3cm} &45\% \\ &\text{Dresses and skirts} &\hspace{3cm} &33\tfrac{1}{3}\% \\ &\text{Bridal and evening gowns} &\hspace{3cm} &50\% \\ &\text{Blouses, jeans, and slacks} &\hspace{3cm} &25\% \end{split}\end{equation}[/latex]
    Lisa and her daughters did a huge closet clean-out and had the following items sold at the consignment store. For each category, calculate the amount for the store fee and the amount Lisa and the girls received. Add your answers to Table 5.13.1.

    Table 5.13.1: Question 14 Complete the Chart

    Question Number	Item	Selling Price	Store Fee	Amount for Lisa & Her Daughters
    a	Wedding dress	$275	—	—
    b	3 dresses at $40 each	3 @ $40 = $120	—	—
    c	Lisa’s winter coat at $120	$120	—	—
    d	4 pairs of outgrown jeans at $10 each	4 @ $10 = $40	—	—

5.13: Review Answers

1. 45 marks
2. $40000
3. Restaurant:
   1. $25.80
   2. $77.40
4. $457.14
5. 15000 tickets
6. 6.6% increase
7. 21.7% depreciation
8. $322.32
9. 181.3% mark-up
10. 90% correct
11. Ski jackets:
    1. $126.47
    2. $141.65
12. 26.5% increase
13. Tax:
    1. $30.78
    2. $33.86
    3. $7.76
    4. $72.40

14. Table 5.13.2: Question 14 Answers

    Question Number	Item	Selling Price	Store Fee	Amount for Lisa & Her Daughters
    a	Wedding dress	$275	$137.50	$137.50
    b	3 dresses at $40 each	3 @ $40 = $120	$40.00	$80.00
    c	Lisa’s winter coat at $120	$120	$54.00	$66.00
    d	4 pairs of outgrown jeans at $10 each	4 @ $10 = $40	$10.00	$30.00

Attribution

This chapter has been adapted from Unit 4 Review: More Working with Percent in Adult Literacy Fundamental Mathematics: Book 6 – 2nd Edition (BCcampus) by Liz Girard and Wendy Tagami (2022), which is under a CC BY 4.0 license.