Ch. 10, 11 Ratios & Percentages

Question 1

Direct variation (“y varies directly with x”) formula

Answer 1

y = kx

Question 2

Inverse variation (“y varies inversely with x”) formula

Answer 2

y = k/x

Question 3

“y varies directly with x but inversely with z”

Answer 3

y = kx/z

Question 4

Steps when adding/subtracting to achieve a desired ratio (for example, boys to girls is 4 to 5, how many boys do we need to add to make the ratio 3 to 4?)

Answer 4

1. Get the actual amounts (not just the ratio/ relationship; if you don’t know actuals, do variables like “4x”)
2. Add/subtract amount or variables
3. Set equal to new ratio

Question 5

What are two methods for solving ratio problems?

Answer 5

1. Set up ratio multiplier, solve for multiplier
2. Set up a proportion & cross multiply

Question 6

What are the steps to solve this question:
A park contains cats and dogs. 60% of cats are over 1 year old and 60% of dogs are under 1 year old. If 45% of the total cats and dogs are over 1 year old, dogs are what fraction of the total cats and dogs at the park?

Answer 6

1. Determine the percentage of cats and dogs (individually) that are over 1 year old:
   60% of cats and 40% of dogs
2. Determine the number of cats AND dogs (together) over 1 year old: 45% of cats and dogs
3. Set up an equation/ ratio, the number of cats & dogs over 1 year old OVER the total number of cats & dogs = 45%:
   [(60/100)C + (40/100)D] / C + D = (45/100)
4. Solve to get a relationship b/w cats & dogs, then solve for D / C+D

Question 7

Translate to math: “a is what percent of b?”

Answer 7

a = (x/100) x b
OR
x = (a/b) x 100

Question 8

Percent less than formula

Answer 8

Final Value = Initial Value x (1 - “percent less than” / 100)

Question 9

Percent greater than formula

Answer 9

Final Value = Initial Value x (1 + “percent greater than”/100)

Question 10

Percent change formula

Answer 10

Percent change = ((Final Value - Initial Value)/ Initial Value) x 100

Question 11

800% greater than z =

Answer 11

(1+800/100) x z
= ((100+800)/100) z
= (900%)z = 9z

800% greater than z = 900% of z

Question 12

x% of y =

Answer 12

y% of x

Question 13

Increase m by x%

Answer 13

= m (1 + x/100)

Question 14

Decrease m by x%

Answer 14

= m (1 - x/100)