Percent Proportions, Ratios and Proportions, Rates and Unit Rates Direct Proportion and Constant of Proportionality

What is the formula for solving percent problems?

is/of = percent/100

If 18 is what percent of 42, how do you find the percentage?

Set up the proportion

18/42 = x/100

To get:

18 × 100=42 × x,

solve for x to get

x≈42.86%.

How do you find what percent 20 is of 45?

Set up the proportion

20/45 = x/100

cross-multiply to get

20 × 100=45 × x

solve for x to get

x≈44.44%.

What percent of 12 is 27?

Set up the proportion

27/12 = x/100

cross-multiply to get

27 × 100=12 × x, solve for x to get

x=225%.

How do you solve a proportion problem such as "Carmen can read 4 books in 10 hours. How many hours to read 50 books?"

Set up the proportion

4 books/ 10 hours = 50 books/ x hours

cross-multiply to get

4 × x=50 × 10

solve for x to get

x=125 hours.

What does the ratio of boys to girls in a class being 8 to 7 imply?

It implies that for every 8 boys, there are 7 girls.

How do you determine miles per day if you travel 36 miles in 4 days?

Set up the ratio

36 miles/4 days

simplify to find the answer

9 miles per day

How do you find the dollar rate per hour if you earn $96 in 8 hours?

Set up the ratio

96 dollars/ 8 hours

simplify to find the answer

$12 per hour

What is the equation for a direct proportion?

y=kx

Is y=2x an example of a direct proportional relationship? Why or why not?

Yes, it is a direct proportional relationship because as

x increases, y increases at a constant rate of 2.

What type of relationship is y=3x+10?

It is a non-direct proportional relationship because of the additional constant term +10, which means the relationship is not purely linear through the origin.

Why is y=8 considered a non-direct proportional relationship?

Because y is constant and does not change with

x, so there is no direct proportionality.