Math - Proportionalities

Sarah notices her map has a scale of $\frac{1}{4}; in=1; mile$ . She measures between Beaver Falls and Chipmonk Cove. How far apart are the cities?

Explanation

$\frac{1}{4}; in=1; mile$ is the same as

So to find out the distance between the cities

$12.5; in \cdot \frac{4; miles}{1;in }=50; miles$

Sarah notices her map has a scale of $\frac{1}{4}; in=1; mile$ . She measures between Beaver Falls and Chipmonk Cove. How far apart are the cities?

Explanation

$\frac{1}{4}; in=1; mile$ is the same as

So to find out the distance between the cities

$12.5; in \cdot \frac{4; miles}{1;in }=50; miles$

Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?

(1 gallon = 4 quarts)

Explanation

First set up the proportion:

$\frac{3; parts ; yellow}{1 ; part; red}=\frac{x ; quarts ; yellow}{2 ; quarts ; red}$

x =

Then convert this to gallons:

$6 ; quarts; \cdot \frac{1 ; gallon}{4; quarts}= 1.50; gallons$

Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?

(1 gallon = 4 quarts)

Explanation

First set up the proportion:

$\frac{3; parts ; yellow}{1 ; part; red}=\frac{x ; quarts ; yellow}{2 ; quarts ; red}$

x =

Then convert this to gallons:

$6 ; quarts; \cdot \frac{1 ; gallon}{4; quarts}= 1.50; gallons$

If is inversely proportional to , and if when , find a formula for .

$y=\frac{16}{x}$

$\frac{16}{y}=x$

$y=\frac{x}{16}$

Explanation

Since y is inversely porportional to x, you can use the standard equations of $y=\frac{k}{x}$ where k is a constant. Plugging the given x and y into this equation to solve for k, . To get the answer, substitute k into the standard equation.