Chapter 12: Percent Word Problems

what is the percent profit equation?

P/C x 100

what is the profit equation?

P=R-C

a store is selling shirts at a profit of 75% of the wholesale purchase price. If the selling price of each shirt is $35 how much did the store pay for one shirt?

profit per shirt= 0.75C

P=0.75C

R=$35

0.75C=35

C=35/1.75

C= $20

what does the phrase percent of mean?

the multiplication of a given percent by a given number

what is 400 percent of y

400/100 x y = 4y

what is ½ a percent of 100

1/2/100 × 100 = 1/200×100 = 0.5

what are the two ways that “what percent” problems can be represented?

a variable divided by 100 x/100

we can use the expression a/b x 100

20 is what percent of 80

20 =( x/100 ) 80

120 is what percent of 30?

120/30 × 100 = 400

what is the percent less equation?

final value = initial value x (1-percent less than / 100)

to solve percent less problems, subtract the percent from 100. For example, 65% less means

100-65 = 35% of the initial value

what is the percent greater equation?

final value = initial value x (1+percent greater than /100)

an item originally priced at n dollars is marked up by 40%. The new price is what percent of the original price?

n x (1+ 40/100)

(n) x (100+40/100)

1.4n = 140% of n

what is 24% of 25?

¼ x 24 = 6

x percent of y = y percent of

x

38.2% of 79,126 = 79,126% of

38.2

when given a fractional percentage change you must still divide that percentage by

100

a percent increase of n percent is equivalent to multiply by

(1+n/100) = 100+n/100

when a value undergoes multiple percent changes, what do you have to do?

multiply the original value by the multiplier for each change in sequence

an item originally priced at $100 was marked up by 20%, and the new price is then marked up by another 20%

(100×120/100) x 120/100 = 144

an increase of 10% followed by a decrease of 10% would be calculated as:

10% increase: 1.10x

10% decrease: 1.10x(0.9) = 0.99x

what is the percent change formula?

[(final value - initial value) / initial value] x 100

in june, a painting was valued at $1,000. by july its value had risen to $7,000. what was the percent change in the painting’s value from june to july?

(7000-1000/1000) x 100 = 600%

the price of an item was decreased by 20%. by what percent must the discounted price be increased to return to the original price?

if x=the original price, then a 20% decrease makes the discounted price 0.8x

to find the percent increase required to return to 0.8x:

[(x - 0.8x) / 0.8x] x 100

(0.2x/0.8x) x 100 = 25%

what are the two methods we can use to find a percent of an unknown amount?

represent the unknown amount by a variable

assume the unknown amount is 100

if 80% of the students at an elementary school are girls, what percent are boys?

80/100 × 100 = 80

100-80 = 20

20/100= 20%

if the price of an item was increased by 50% by what percent must the marked up price be decreased to return to its original price

a 50% increase makes the marked-up price 1.5x

(x-1.5x/1.5x ) x 100 = (-0.5x/1.5x) x 100

(-1/3) x 100 = -33 1/3%