percent x whole = partpercent x whole = part

ExerciseExerciseWrite the percent formula.Write the percent formula.

5.15.1What is 17% of 30?What is 17% of 30?

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What percent of 30 is 24?What percent of 30 is 24? 80%80%

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70% of what number is 35?70% of what number is 35? 5050

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If you remove 30% of the items, what percent of the items are left?

If you remove 30% of the items, what percent of the items are left? 70%70%

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Find the discount and sales price if the retail price is $27.80 and the discount rate is 15%.

Find the discount and sales price if the retail price is $27.80 and the discount rate is 15%.

= $23.63= $23.63

discount = rate x retail pricediscount = 0.15(27.80)

= $4.17sale price = retail – discountsale price = $27.80 – $4.17

Example 1Example 1

An item originally priced at $45 sold for $32.85. What was the discount rate?

An item originally priced at $45 sold for $32.85. What was the discount rate?

= 27%= 27%

rate x retail price = discount45 – 32.85 = $12.15

45p = 12.154545 4545

p = 0.27

Example 2Example 2

Find the discount if the retail price is $50 and the discount rate is 18%.

Find the discount if the retail price is $50 and the discount rate is 18%. $9$9

ExampleExample

Find the discount rate if the retail price is $75 and the discount is $15.

Find the discount rate if the retail price is $75 and the discount is $15. 20%20%

ExampleExample

Find the discount and the discount rate if the retail price is $80 and the item is on sale for $55.

Find the discount and the discount rate if the retail price is $80 and the item is on sale for $55.

discount: $25discount rate: 31.25%

discount: $25discount rate: 31.25%

ExampleExample

During a going-out-of-business sale, a company decides to reduce its merchandise 10% per week until it is all sold. For example, a $100 item sells for $90 the first week, $81 the second week, and so on. What is the cost of a $250 TV set if is still there the third week?

During a going-out-of-business sale, a company decides to reduce its merchandise 10% per week until it is all sold. For example, a $100 item sells for $90 the first week, $81 the second week, and so on. What is the cost of a $250 TV set if is still there the third week?

ExampleExample

$182.25$182.25

What is the retail price if the sale price is $80 after a 33% discount?

What is the retail price if the sale price is $80 after a 33% discount? $119.40$119.40

ExampleExample

What is the retail price if the cost is $40 and the markup rate is 25%?

What is the retail price if the cost is $40 and the markup rate is 25%? $50$50

ExampleExample

Cost is the amount a merchant pays for the merchandise he will sell.

Cost is the amount a merchant pays for the merchandise he will sell.

CostCost

Retail price is the regular amount a merchant asks his customer to pay for merchandise.

Retail price is the regular amount a merchant asks his customer to pay for merchandise.

Retail PriceRetail Price

Markup is the amount the merchant adds to his cost to arrive at the retail price.

Markup is the amount the merchant adds to his cost to arrive at the retail price.

MarkupMarkup

Markup rate is the amount of markup on an item as a percent of its cost.

Markup rate is the amount of markup on an item as a percent of its cost.

Markup RateMarkup Rate

markup = markup rate x costmarkup = markup rate x cost

retail price = cost + markupretail price = cost + markup

A merchant buys shirts at $28 each and uses a 25% markup rate. Find the markup amount and retail price.

A merchant buys shirts at $28 each and uses a 25% markup rate. Find the markup amount and retail price.

= $35= $35

markup = markup rate x cost= 0.25(28) = $7

retail price = cost + markup= 28 + 7

Example 3Example 3

A merchant buys ties for $15 and sells them for $18. Find the markup and markup rate.

A merchant buys ties for $15 and sells them for $18. Find the markup and markup rate.cost + markup = retail price

15 + m = 18

m = 315 + m – 15 = 18 – 15

The markup is $3.The markup is $3.

Example 4Example 4

A merchant buys ties for $15 and sells them for $18. Find the markup and markup rate.

A merchant buys ties for $15 and sells them for $18. Find the markup and markup rate.

The markup rate is 20%.The markup rate is 20%.

markup rate x cost = markupp x 15 = 3

15p = 31515 1515

p = 0.2 = 20%

Example 4Example 4

If the cost is $45 and the retail price is $65, what is the markup and the markup rate?

If the cost is $45 and the retail price is $65, what is the markup and the markup rate?

markup: $20; markup rate: 44.4%

markup: $20; markup rate: 44.4%

ExampleExample

In an “everything is a dollar” store, what is the most a store owner can buy his merchandise for if he wishes to make a 20% profit?

In an “everything is a dollar” store, what is the most a store owner can buy his merchandise for if he wishes to make a 20% profit? $0.83$0.83

ExampleExample

Jody wants to buy a road bike for racing. The manager of OutBike bicycle shop just got in a new shipment of road bikes, and the one Jody is interested in costs the store $1,480. The manager marks the bike up 40%.

Jody wants to buy a road bike for racing. The manager of OutBike bicycle shop just got in a new shipment of road bikes, and the one Jody is interested in costs the store $1,480. The manager marks the bike up 40%.

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What is the retail price of the road bike that Jody is interested in?

What is the retail price of the road bike that Jody is interested in? $2,072$2,072

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After three months the manager advertises a 20% off sale on all bikes in the store. How much would the bike that Jody wants cost during this sale?

After three months the manager advertises a 20% off sale on all bikes in the store. How much would the bike that Jody wants cost during this sale? $1,657.60$1,657.60

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Three months after the first sale the manager takes an additional 20% off the sale bikes. How much would the bike cost at this point?

Three months after the first sale the manager takes an additional 20% off the sale bikes. How much would the bike cost at this point?

$1,326.08$1,326.08

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Jody talked to the manager about the bike, and he told her she could have the bike for either 40% off the original price or the price after both 20% discounts are taken off. Which should she choose?

Jody talked to the manager about the bike, and he told her she could have the bike for either 40% off the original price or the price after both 20% discounts are taken off. Which should she choose?

40% off the original price40% off the original price

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Why is the price after two 20% discounts are taken of different from the price when a 40% discount is taken off?

Why is the price after two 20% discounts are taken of different from the price when a 40% discount is taken off?

The second 20% is figured on the sale price, which is smaller than the original

retail price.

The second 20% is figured on the sale price, which is smaller than the original

retail price.

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How does the 40% discount compare to the cost of the bike before the markup? Why are these amounts different?

How does the 40% discount compare to the cost of the bike before the markup? Why are these amounts different?

The 40% discount is figured on the higher retail price,

whereas the 40% markup is figured on the lower cost.

The 40% discount is figured on the higher retail price,

whereas the 40% markup is figured on the lower cost.

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