Every time you buy a snack, choose between two brands or sell something at a school fair, you are doing consumer arithmetic – the maths of money. In this lesson you will find different combinations of Trinidad and Tobago bank notes that make $1000, decide which item is the best buy, and work out profit, loss and percentage profit or loss. You will need the decimal and percentage skills from Decimal Calculations and Percentages. All amounts are in TT dollars.

Making $1000 with bank notes

Trinidad and Tobago has $5, $10, $20, $50 and $100 notes. There are many ways to make the same total. The simplest use just one kind of note:

Note	Number needed for $1000	Working
$100	10	1000 ÷ 100
$50	20	1000 ÷ 50
$20	50	1000 ÷ 20
$10	100	1000 ÷ 10
$5	200	1000 ÷ 5

You can also mix notes. For example: 5 × $100 + 10 × $50 = $1000; 9 × $100 + 1 × $50 + 2 × $20 + 1 × $10 = $1000; and 4 × $100 + 6 × $50 + 10 × $20 + 6 × $10 + 8 × $5 = $1000 (that one uses 34 notes). A tidy way to find combinations is a table: start with the biggest note, decide how many to use, and fill the rest with smaller notes. Using only $5, $10, $20, $50 and $100 notes, there are 59 576 different ways to make $1000 – far too many to list, which is why we look for patterns instead.

Best buy: comparing unit prices

Shops often sell the same product in different sizes. The bigger pack is not always cheaper for each gram or millilitre. To find the best buy, compare unit prices: the cost of one unit (1 kg, 1 L, 100 g or one item). Divide the price by the quantity. Another method is to scale the packs up to the same quantity and compare the totals.

Item	Price	Price per litre
250 mL box of juice	$3.50	$3.50 × 4 = $14.00
1 L carton	$11.95	$11.95
Pack of 6 × 250 mL (1.5 L)	$18.00	$18.00 ÷ 1.5 = $12.00

Remember that the unit price tells you about value for money, not about quality. The best buy for you also depends on how much you need, whether it will spoil before you finish it, how much you can carry, and how much money you have today.

Profit and loss

• The cost price (CP) is what the seller paid for the item. The selling price (SP) is what the customer pays.
• If SP is more than CP, the seller makes a profit: profit = SP − CP.
• If SP is less than CP, the seller makes a loss: loss = CP − SP.
• Percentage profit = profitcost price × 100% and percentage loss = losscost price × 100%. Always divide by the cost price.

To find a selling price from a percentage profit, start from the cost price as 100%: a 25% profit means SP = 125% of CP. A 30% loss means SP = 70% of CP. Working backwards, if you know SP and the percentage, divide: CP = SP ÷ 1.25 for a 25% profit.

Worked examples

Example 1: Best buy for rice

Question: A 2 kg bag of rice costs $22.50 and a 5 kg bag costs $54.95. Which is the better buy?

1. 2 kg bag: $22.50 ÷ 2 = $11.25 per kg.
2. 5 kg bag: $54.95 ÷ 5 = $10.99 per kg.

Answer: The 5 kg bag is the better buy (26 cents less per kilogram).

Example 2: Same-quantity method

Question: Pack A has 3 chocolate bars for $10. Pack B has 5 of the same bars for $16. Which is better value?

1. The LCM of 3 and 5 is 15 bars.
2. 15 bars from Pack A: 5 packs × $10 = $50. From Pack B: 3 packs × $16 = $48.
3. Check with unit prices: A is about $3.33 a bar, B is $3.20 a bar.

Answer: Pack B.

Example 3: Selling mangoes

Question: Ms Joseph buys a crate of 50 Julie mangoes for $75 and sells them all at $2.50 each. Find her profit and percentage profit.

1. SP = 50 × $2.50 = $125.
2. Profit = $125 − $75 = $50.
3. Percentage profit = 5075 × 100% = 6623%.

Answer: Profit $50, which is 6623% (about 66.7%).

Example 4: A loss

Question: Darren bought a phone for $1200 and sold it a year later for $960. Find his loss and percentage loss.

1. Loss = $1200 − $960 = $240.
2. Percentage loss = 2401200 × 100% = 20%.

Answer: A loss of $240, or 20%.

Example 5: A doubles stand

Question: Each doubles costs a vendor $3.20 to make and sells for $6.00. Find the profit on one doubles, the percentage profit, and the profit on 150 doubles.

1. Profit on one: $6.00 − $3.20 = $2.80.
2. Percentage profit = 2.803.20 × 100% = 87.5%.
3. On 150: 150 × $2.80 = $420.

Answer: $2.80 each (87.5%); $420 for 150.

Example 6: Selling price from a percentage

Question: A shop buys a school bag for $80 and wants a 25% profit. What should it charge?

1. SP = 125% of $80 = 1.25 × 80.

Answer: $100.

Example 7: Cost price from a percentage

Question: A cooler sells for $150, giving the shop a 25% profit. What was the cost price?

1. $150 is 125% of the cost price.
2. CP = 150 ÷ 1.25 = 120.
3. Check: 25% of $120 is $30, and $120 + $30 = $150 ✓.

Answer: $120.

Common mistakes

• Dividing by the selling price for percentage profit. Use the cost price.
• Comparing pack prices instead of unit prices. A cheaper pack may hold much less.
• Mixing units when comparing: change 250 mL and 1 L to the same unit first.
• Taking 25% off the selling price to find the cost price. $150 − 25% of $150 is $112.50, not $120.

Practice questions

Try these yourself first, then open each answer to check your working.

Quick check

Next: Consumer Arithmetic: VAT, Discounts and Simple Interest

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 1, Term 3, Strand 1.1 Number Operations and Number Theory, Topic 1.1.6 Consumer Arithmetic – Learning Outcomes 1.1.6.1 (combinations of $5, $10, $20, $50 and $100 notes that make $1000), 1.1.6.2 (finding the best buy among similar items by price) and 1.1.6.3 (percentage problems – here profit, loss and percentage profit and loss).

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