percents

A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $24. What is the principal on the loan.

24 = 8/100 (x) x = 300

A stereo was marked down by 30% and sold for $84. What was the resale price of the stereo?

(x)(70/100) = 84 84 x (100/70) = x 84 x (10/7) = x x = 120

Common word translations

percent = divide by 100 = /100 of = multiple = x is = equals = what = unknown value = x, y, z, or any variable e.g. What is 70 percent of 120? x = 70/100 x 120. x = 7/10 (120) x = 7 x 12 x = 84 e.g. thirty is what percent of 50 30 = x/100 x 50 30/50 = x/100 30/50 (100) = x x = 60

A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 200mm of rum. How much guava juice is in the bottle? (a) 360 (b) 480 (c) 600 (d) 720 (e) 900

80% of the bottle is filled with that mixture. But 20% = 200. So 80% in a total liquid number = 800. Now, we have to figure out how much of that 800 is guava. 60% of 800. This can be done through benchmarks. 10% is 80 x 6 = 480.

Company x has exactly two product lines and no other sources of revenue. If the consumer product line experiences k% increase in revenue (where k is a positive integer) in 2015 from 2014 levels and the machine parts line experiences a k% decrease in revenue in 2015 from 2014 levels, did Company's overall revenue increase or decrease in 2015. (1) In 2014, the consumer products line generated more revenue than the machine parts line. (2) k = 8

All we have is percent increases. We need the original numbers of both to determine whether or not the revenue overall increased or decreased. If both lines have the same number, then there is no difference. If CP line > MP line, total increase If CP line < MP line, total decrease. (1) tells us that CP > MP, so yes this is sufficient, tell us that overall revenue increased. (2) insufficient, we still need to know the original value. Answer is A. only (1) is sufficient.

What is 18% of 50? What is 40% of 30? What is 75% of 20?

20% is easy = 10. 1% is easy = .5 .5(2) to get 2% = 1. 10 - 1 = 9. 10% = 3. 3 x 4 = 12 50% = 10. Half of that is 5. 10+5 = 15

Company Z sells only chairs and tables. What percent of its revenue in 2008 did Company Z derive from its sales of chairs? (1) in 2008, the price of tables sold by Company z was 10% higher than the price of chairs sold by company z (2) in 2008, Company Z sold 20% fewer tables than chairs.

We want to know: Revenue of chairs / total revenue total revenue = revenue of chairs + revenue of tables Revenue = price x quantity sold Statement 1 tells us relative price but no quantity. Statement 2 tells us relative quantity but no price. But together, they give us relative quantity and relative price, which can give us relative revenue. B is the answer.

Increasing or decreasing from the original e.g. What number is 50% greater than 60?

You can rewrite this. Remember: 10% increase = 110% of the original 10% greater than = 110% of the original 45% decrease = 55% of the original 45% less than = 55% of the original What number is 150% of 60? x = 150/100 x 60 x = 90 You can also use benchmarks. 50% is 30 x 3 = 90.

If 800 is increased by 50% and then decreased by 30% what is the resulting number?

You can use benchmarks. increased by 50% would make it 1200 and then 10% of that is 120 x 3 = 360. 1200 - 360 = 840 Can also use multiplication (150/100) x (70/100) = 105 / 100 = 5% increase which is 40. So if you add that you get 840

If x is 40% of y and 50% of y is 40, then 16 is what percent of x?

work backwards. 50% of y is 40 y= 80. x is 40% of (80) now use benchmarks. 10% is 8 x 4 = 32. 16 = x/100 (32) 50%

If 1,500 is increased by 20% and then reduced by y%, yielding 1,080, what is y?

1,500 increased by 20% can be done through benchmarks. 10% = 150 x 2 = 300 So, the new number is 1,800. Now, you are just looking for the percent change. 1800 - 1080 / 1800 40% change.

The cost of a plane ticket is increased by 25%. Later the ticket goes on sale and the price is reduced 20%. What is the overall percent change in the price of the ticket.

Can be solved with benchmark numbers. But also, can use multiplication (125/100) x (80/100) = no percent change.

Percent Change e.g. Coffee increased from 80 cents to 84 cents. What was the percent in price change.

Change in Value / Original Value 84 - 80 / 80 4/80 = 1/20 x/100 = 1/20 20x = 100 x = 5

Successive percent change e.g. If a ticket increased in price by 20%, and then increased again by 5%, by what percent did the ticket price increase in total?

It is NOT just adding the two percents. You have to calculate each piece separately. Use number 100. Increases to 120. And then another 5% increase increased it to 126. The percent increase is 26% You can also multiply the changes together to get the answer. (120/100) x (105/100) = 126/100

A bowl is half full of water. Four cups of water are then added to the bowl, filling the bowl to 70% of its capacity. How many cups are now in the bowl?

Started at 50%. Four cups increased it to 70%. So, four cups is a 20% increase. So, if 20% = 4 cups, how much is 70%? Use benchmarks. 4 x 3 = 12. 10% is 2. 14%.

Percent benchmarks

Use shortcuts to arrive at percentages by breaking it up. e.g. What is 15% of 90. Well 10% of 90 is easy = 9. 5 % is just half of that. 4.5. Add the two to get 15% = 13.5 e.g. What is 6 percent of 50? 5% of 50 is 2.5. 1% of 50 is .5 Add them = 3

To find the new price e.g. If the price of a $30 shirt is decreased by 20%, what is the final price of the shirt?

Use the new percent, not the decrease in percent. new percent = new value/ original value. If price decreased by 20%, then the new price is 100% - 20% - 80% of the original. 80% = x / 30 4/5 = x/30 x = 24 You can also solve this specific one with percent benchmarks. 10% is 3. times 2 is 6. $6 off the original price.