Money & prices
Totals, change, discounts, and changes on top of changes.
In your head, jot if needed · no calculator why?
Opens at level 13. You're level 1. You can read and practice here now.
the idea
Money is decimals with two places: cents are hundredths of a dollar. Keep dollars and cents apart, and remember that every 100 cents carry over as one dollar.
With percents, keep two questions apart: how much comes off or goes on (the change) and what you pay (the final price). A price after one change is the new starting point for the next. That is why a 10% rise and a 10% cut don't cancel: 100 goes up to 110, then down to 99.
techniques
Dollars first, then cents
- Add the whole dollars.
- Add the cents. Every 100 cents make one more dollar.
- Put the two together.
worked example
$8.60 + $14.75
- Dollars: $8 + $14 = $22.
- Cents: 60¢ and 75¢ make 135¢, which is $1.35.
- $22 + $1.35 = $23.35.
Answer: $23.35
Count up to make change
- Count up from the price to the next whole dollar.
- Count on from there to the amount paid.
- Add the two jumps.
worked example
You pay $50 for a $31.40 item. How much change do you get?
- $31.40 up to $32 is 60¢.
- $32 up to $50 is $18.
- Change: $18.60.
Answer: $18.60
One change at a time
- Find the change: the percent of the current amount.
- Take it off for a discount, or add it for an increase. That gives the final price.
- For a second change, start from the new amount, not the original.
- Or multiply: 20% off is × 0.8, and 10% up is × 1.1.
worked example
Increase 200 by 10%, then decrease the result by 20%. What is the final amount?
- Up 10%: 200 × 1.1 = 220.
- Down 20% of the new amount: 220 × 0.8 = 176.
Answer: 176
watch out for
- Forgetting to carry a dollar. 50¢ and 75¢ make $1.25, so $12.50 + $7.75 is $20.25, not $19.25.
- Taking away only the dollars for change. Paying $20 for $13.75, the 75¢ uses up one of the dollars: $6.25, not $7.25.
- Giving the discount instead of the final price. 15% off $80 takes $12 off, so you pay $68.
- Assuming equal changes cancel. Up 10% and then down 10% ends below where you started.
practice
Money totals
worked example
$40.20 + $55.50 + $12.90
Answer: $108.60
- The cents make $1.60: 20¢ + 50¢ + 90¢ = 160¢.
- Dollars first, then cents: $107 + $1.60 = $108.60.
Making change
worked example
You pay $20 for a $13.25 item. How much change do you get?
Answer: $6.75
- Count up: $13.25 → $14 is 75¢, and $14 → $20 is $6.
- Change: $6.75.
Final price
worked example
What is the final price after 20% off $362?
Answer: $289.60
- 20% of $362 is $72.40.
- $362 − $72.40 = $289.60.
Change after change
worked example
Increase 100 by 20%, then decrease the result by 25%. What is the final amount?
Answer: 90
- 100 × 1.2 = 120, then 120 × 0.75 = 90.
- The second percent is taken of the new amount, 120, not of 100.