Question

Write a proportion for the statement.

$118 per week is proportional to $472 per 4 weeks. The proportion is _____?

Answer 1

Writing Proportions

A proportion is a mathematical comparison between two ratios.

A ratio is a comparison between two numbers.

For instance, the ratio of apples to bananas in a fruit basket is 1 apple to 2 bananas:

• 
  `\frac{1\hspace{3}apple}{2\hspace{3}bananas}`

This is proportional to the ratio of apples to bananas in another fruit basket, which is 2 apples to 4 bananas:

• 
  `\frac{2\hspace{3}apples}{4\hspace{3}bananas}`

To write a proportion from this information, we can compare the ratios by makign them equal to each other:

• 
  `\frac{1\hspace{3}apple}{2\hspace{3}bananas}=\frac{2\hspace{3}apples}{4\hspace{3}bananas}`
• 
  `(1)/(2)=(2)/(4)`

Solving the Question

We're given:

• $118 per week
• $472 per 4 weeks
• These are proportional

$118 per week is one ratio:

• 
  `\frac{118\hspace{3}dollars}{1\hspace{3}week}`

$472 per 4 weeks is another ratio:

• 
  `\frac{472\hspace{3}dollars}{4\hspace{3}weeks}`

Now, set them equal to each other to create a proportion:

• 
  `\frac{118\hspace{3}dollars}{1\hspace{3}week}=\frac{472\hspace{3}dollars}{4\hspace{3}weeks}\\\\(118)/(1)=(472)/(4)`

Answer:

Therefore, the proportion is
`(118)/(1)=(472)/(4)`.