Percent Proportions & Equations

90% of what is 342?

Answer: Proportion: 90/100 = 342/n Equation: 0.9 ∙ n = 342 n = 380

24% of 300 is what?

Answer: Proportion: 24/100 = n/300 Equation: 0.24 ∙ 300 = n n = 72

Find 320% of 60.

Answer: Proportion: 320/100 = n/60 Equation: n = 3.2 ∙ 60 n = 192

45 is 60% of what?

Answer: Proportion: 60/100 = 45/n Equation: 45 = 0.60 ∙ n n = 75

What percent of $4000 is $64?

(remember to convert the decimal to percent by multiplying by 100%) Answer: Proportion: n/100 = 64/4000 Equation: n ∙ 4000 = 64 (remember to convert the decimal to percent by multiplying by 100%) n = 1.6%

How much tax will Carter pay on a surround-sound system that cost $1885.00 if the tax is 5%

Answer: n = $94.25 Proportion: 5/100 = n/1885 Equation: n = 0.05 ∙ 1885 n = $94.25

Bob now earns $9.50 per hour. This is 125% of what she earned last year. What did she earn per hour last year?

Answer: Proportion: 125/100 = 9.5/n Equation: 9.5 = n ∙ 1.25 n = $7.60

I paid $8400 in federal and state income taxes last year, which amounted to 28% of my annual income. What was my income last year?

Answer: n = $30,000 Proportion: 28/100 = 8400/n Equation: 8400 = 0.28 ∙ n n = $30,000

Commission, markup, discount, tax, tip, etc.

Find the commission: You sold a car for: $30,000 Commission: 3%

Answer: Sale price = $30,000 Commission = $30,000 ∙ 0.03 = $900 = $900

Find the final price: Cost of a sled: $99.50 Markup: 95%

Answer: = $194.03 Cost = $99.50 Markup = 99.50 ∙ 0.95 = $94.53 Final: $99.50 + $94.53 = $194.03

Find the final price: Original price of concert tickets: $100.00 Discount: 21%

Answer: = $79 Cost = $100.00 Discount = 100 ∙ 0.21 = $21.00 Final: $100 - $21 = $79

Find the final price: Original cost of book: $49.95 Tax: 3%

Answer: = $51.45 Cost = $49.95 Tax = 49.95 ∙ 0.03 = $1.50 Final: $49.95 + $1.50 = $51.45

Find the final price: Original cost of meal: $49.95 Tax: 3% Tip: 15%

Answer: =$59.17 Cost = $49.95 Tax = 49.95 ∙ 0.03 = $1.50 Cost of meal = $49.95 + $1.5 = $51.45 Tip: $51.45 ∙ 0.15 = $7.72 Final cost = $51.45 + $7.72 =$59.17

Percent Change

A percent of change is the percent a quantity increases or decreases from its original amount.

% change = (positive difference)/a From a to b. % change = (positive difference)/a Example: From 82 to 38 (82-38)/82 = 0.537 = 53.7% decrease

Find the Percent Change. State if it is an increase or decrease Find the Percent Change. State if it is an increase or decrease. Round answer to the nearest tenth of a percent.

From 75 to 45.

From 75 to 45 (75-45)/75 = 0.40 = 40% decrease

From 58.5 to 76.3

From 58.5 to 76.3 (76.3-58.5)/58.5 = 0.304 = 30.4% increase

Ratios Rates Proportions

Solve: ― = ― 10 k 8 4

Answer: k = 5

Conversion Word Problems

How many inches are equal to 8 yards?

8 yds ∙ 3ft/1yd ·12in/1ft = 288 inches Answer: 8 yds ∙ 3ft/1yd ·12in/1ft = 288 inches

How many inches are equal to 2 miles?

Answer: 2 miles ∙ 5280ft/1mi ·12in/1ft = 126,720 inches

How many seconds are equal to 2 years?

2 yr∙(365days/1yr)·(24hr/1day)·(60min/1hr)· Answer: 2 yr∙(365days/1yr)·(24hr/1day)·(60min/1hr)· (60sec/1min)= 63,072,000 seconds

How many cups are in 5 gallons?

5 gal∙(4qt/1gal)·(2pint/1qt)·(2cups/1pint)= Answer: 5 gal∙(4qt/1gal)·(2pint/1qt)·(2cups/1pint)= 80 cups

I am making some math videos I am making some math videos. I shoot 10 “takes” for each video and expect to make 144 videos per book. I have 11 books. Each “take” averages 5 minutes. If I shoot continuously, how many days will it take me to make a full set of videos for all the books?

11bk∙(144vid/1bk)·(10takes/1vid)·(5min/1take)· Answer: 11bk∙(144vid/1bk)·(10takes/1vid)·(5min/1take)· (1hr/60min)·(1day/24hr) 55 days

Similar Figures

Polygon is a closed plane figure formed by 3 or more line segments that do not cross. Two polygons are similar polygons if: corresponding angles have the same measure. the lengths of the corresponding sides form equivalent ratios.

Example: BC/GH = AC/FH (Text Book) 50/75 = 40/60 or BC/AC = GH/FH 50/40 = 75/60

Each pair of figures are similar. Find the missing side. 14 2 x 1

Answer: ― = ― x = 7 x 14 1 2

Similar Figures Word Problems

Brayden reduced the size of a rectangle to a height of 2 inches Brayden reduced the size of a rectangle to a height of 2 inches. What is the new width if it was originally 24 inches wide and 12 inches tall?

Answer: ― = ― x = 4 inches 24 12 x 2

You can use indirect measurement to measure distances that are difficult to measure directly by using proportions and similar figures.

A 6 ft tall person standing near a flagpole cast a shadow 4. 5 ft long A 6 ft tall person standing near a flagpole cast a shadow 4.5 ft long. The flagpole casts a shadow 15 ft long. What is the height of the flagpole?

Answer: ― = ― 4.5 ∙ x = 6 ∙ 15 x = (6 ∙ 15)/4.5 x = 20 x 6 15 4.5

Scale Drawings

A scale drawing is an enlarged or reduced drawing of an object that is similar to the actual object. A scale is the ratio that compares a length in a drawing or model to the corresponding length in the actual object.

The distance of the Rio Grande is 3. 5 inches on a map The distance of the Rio Grande is 3.5 inches on a map. If the map scale is ½ inch = 2 miles, what is the distance of the Rio Grande?

Answer: ― = ― ½ ∙ (x) = 2 ∙ (3.5) ½ x = 7 x = 14 miles ½ 2 3.5 x

Competition Problems

If 8 is 12.5% of x, then x is what percent of 4096? (Round your answer to the nearest whole number.)

Answer: 8 = 0.125 ∙ x 64=x 64 = p ∙ 4096 0.0156 = p 1.56% Round = 2%

A photo 3 inches wide and 5 inches long is being enlarged A photo 3 inches wide and 5 inches long is being enlarged. The new photo is 12 inches long. How many inches wide will it be?

Answer: 7.2

Twenty-five percent of 1200 is fifteen percent of what number?

Answer: 2000

A kavu purse is discounted 25% of it’s original price of $60, during the weekend sale. At the reduced price the store will make a profit of 20% over cost. What was the cost of the purse to the store?

$37.50 Answer: .75(60)=45 Cost + profit = $45 C + 0.2(C) = 45 1.2C =45

The ratio of Auburn to Alabama fans at Cedar Ridge Middle School is 2:5. There are 840 Alabama fans in attendance. How many more Auburn fans would need to enroll to make the ratio of Auburn to Alabama 1:2.

Additional AU fans needed Answer: 2/5 = x/840 x = 336 (Auburn fans) Auburn fans @1/2 = 420 Additional AU fans needed = 420-336 = 84 84

A 42-in flat screen television originally cost $1200 A 42-in flat screen television originally cost $1200. What was its total cost after a 15% discount and an 8% tax rate were applied?

Answer: $1101.60

A polo shirt marked for $48 is offered at a discount of 25% during a sale. At the reduced price, the dealer makes a profit of 20% on the cost. What is the cost to the dealer?

Answer: $30

The ratio of Auburn to Alabama fans at Cedar Ridge Middle School is 2:5. There are 840 Alabama or Auburn fans in attendance. How many more Auburn fans would need to attend to make the ratio (of Auburn to Alabama fans ) 1:2?

Answer: 60

The denominator of a fraction is 3 more than the numerator The denominator of a fraction is 3 more than the numerator. If 25 is added to each, the resulting fraction is equivalent to 0.9. Find the original fraction.

Answer: x/(x+3) (x+25)/(x+3+25)=9/10 x=2 2/5