&KDSWHU0RUH(QULFKPHQW7RSLFVFind a single discount equivalent to each set of successive discounts.
1.40%, 20% 2.25%, 25% 3.10%, 20%, 30%Find a single increase equivalent to each set of successive increases.
4.40%, 20% 5.20%, 40% 6.10%, 20%, 30%7.Discuss and Write Trueor False: A decrease of 10% followed by an increase
of 10% does not change the starting value. Explain your reasoning.page 227 for exercise sets.Enrichment:
Successive Discounts and Increases
Objective To determine the overall percent of change when
more than one percent discount or percent increase is applied.
Two stores in Diego’s town are having sales.
- At Big Bill’s, jeans were discounted 30% last week. This week,
jeans are marked down an additional20%. - At Small Change Shop, everything is 50% off.
The original price of the jeans was $60 at both stores.
Is the sale price the same at both stores?
The sale prices are not the same. One discount of 50% off is a greater discount
than two successive discounts of 30% and 20%. To find a single discount that is
the same as a 30% discount followed by a 20% discount,
follow these steps:
Suppose the original price of an item is p. If you save30%, then you pay70%,
so the price after a 30% discount is 70% of p, or 0.7p.
Applying the second discount, you save 20% of 0.7p. This means you pay80%
of 0.7p. So the final price is 80% of 0.7p, or (0.8)(0.7p), or 0.56p.
The final price, 0.56p, is 56% of p. Paying 56% of the original price is the same
as saving 44%. So a 30% discount followed by a 20% discount is equivalent
to a 44% discount.Big Bill’s- Original Price: $60
- First Markdown: 30% of $60, or $18
First Sale Price: $60 $18 $42 - Second Markdown: 20% of $42, or $8.40
Second Sale Price: $42 $8.40 $33.60
Small Change Shop- Original Price: $60
- 50% off: 50% of $60, or $30
Sale Price: $60 $30 $30