Key terms:

• Price — how much one item costs.
• Total cost — the sum of all the items you bought.
• Payment — the amount you hand to the cashier.
• Change — the money you get back when you paid more than the total cost.

Formulas:

\[ \text{Total cost} = \text{Price} \times \text{Quantity} \]

\[ \text{Change} = \text{Payment} - \text{Total cost} \]

Common banknotes and coins:

When the total includes cents, we usually round to the nearest whole unit.

Example 1: Simple Purchase — Three Items

Problem: Danny bought at the supermarket: bread for $9, milk for $7, and yogurt for $6. How much did he pay in total?

Solution:

1. Item 1: bread — $9
2. Item 2: milk — $7
3. Item 3: yogurt — $6
4. Total cost: \( 9 + 7 + 6 = 22 \).

Answer: Danny paid $22 in total.

Example 2: Calculating Change — Paying with a Banknote

Problem: Riva bought chocolate for $8 and juice for $11. She paid with a $50 bill. How much change did she receive?

Solution:

1. Total cost: \( 8 + 11 = 19 \).
2. Payment: $50.
3. Change: \( 50 - 19 = 31 \).
4. Check: \( 19 + 31 = 50 \) — correct!

Answer: Riva received $31 in change.

Example 3: Multiple Units of the Same Item

Problem: Mum bought 4 bottles of water, each costing $5, and one cake for $34. How much did the whole purchase cost?

Solution:

1. Cost of bottles: \( 4 \times 5 = 20 \).
2. Cost of cake: $34.
3. Total: \( 20 + 34 = 54 \).

Answer: The purchase cost $54 in total.

Example 4: Do You Have Enough Money?

Problem: Gil has $35 in his wallet. He wants to buy a ball for $18 and sunglasses for $22. Does he have enough?

Solution:

1. Total cost: \( 18 + 22 = 40 \).
2. Money in wallet: $35.
3. Comparison: \( 35 \lt 40 \) — he does not have enough.
4. He is short: \( 40 - 35 = 5 \).

Answer: Gil does not have enough money. He is $5 short.

Example 5: Change from a Complex Purchase

Problem: Yael bought 3 notebooks at $7 each and 2 pencils at $4 each. She paid with a $100 bill. How much change does she get?

Solution:

1. Cost of notebooks: \( 3 \times 7 = 21 \).
2. Cost of pencils: \( 2 \times 4 = 8 \).
3. Total cost: \( 21 + 8 = 29 \).
4. Change: \( 100 - 29 = 71 \).
5. Check: \( 29 + 71 = 100 \) — correct!

Answer: Yael will receive $71 in change.

✗ Common mistake: Applying price × quantity only to some items and adding single-unit items directly without thinking.

✓ The correct way: For any item where you bought just one unit, its price goes straight into the total. It helps to make a table listing each item, quantity, and cost before adding everything up.

✗ Common mistake: Calculating change as total cost minus payment (instead of payment minus total cost) and getting a negative number.

✓ The correct way: Change is always: how much you gave minus how much the goods cost, i.e. \( \text{Change} = \text{Payment} - \text{Total cost} \). If the result is negative, there is a mistake.

✗ Common mistake: Forgetting to check whether the available money is enough before calculating change.

✓ The correct way: Always compare first: is payment ≥ total cost? Only if yes can the change be positive.

Key formulas:

• Total cost = \( \text{Price} \times \text{Quantity} \) (for each item), then add them all.
• Change = \( \text{Payment} - \text{Total cost} \)
• Check: \( \text{Total cost} + \text{Change} = \text{Payment} \)

If total cost > payment — you do not have enough money and cannot complete the purchase!