Question

Write a proportion for each statement. A) the numbers -30 and -25 are proportional to the numbers 12 and 10. B) $6.25 per hour is proportional to $187.50 per 30 hr.

Answer 1

Define a proportion: A proportion is a statment that two ratios are the same. For example 2 is to 6 as 8 is to 24. This is a proportion because 2 is the one thrid part of 6 as 6 is the one third part of 24.

The question requires us to write a proportion for each statement.

Statement A: the numbers -30 and -25 are proportional to the numbers 12 and 10. The proportion for this statement is

`\begin{gathered} -30\text{ is to -25 as 12 is to 10} \\ -30\colon-25=12\colon10 \\ This\text{ is the breakdown} \\ (-30)/(-25)=(30)/(25)=(5*6)/(5*5)=(6)/(5) \\ so, \\ -30\colon-25=6\colon5 \\ \text{Also,} \\ 12\colon10=(12)/(10)=(2*6)/(2*5)=(6)/(5) \\ so, \\ 12\colon10=6\colon5 \\ \text{Therefore,} \\ -30\colon-25=12\colon10=6\colon5 \\ -30\colon-25=12\colon10 \end{gathered}`

Statement B: $6.25 per hour is proportional to $187.50 per 30 hr. The proportion for this statement is

`\begin{gathered} \text{ \$6.25 is to one hour as \$187.50 is to 30 hour} \\ \text{This is the breakdown} \\ 6.25\colon1=187.50\colon30 \\ (6.25)/(1)=(625)/(100)=(25*25)/(25*4)=(25)/(4) \\ \text{Also,} \\ 187.50\colon30=(187.50)/(30)=(1875)/(300)=(75*25)/(75*4)=(25)/(4) \\ \\ \text{Therefore,} \\ 6.25\colon1=187.50\colon30=25\colon4 \\ 6.25\colon1=187.50\colon30 \end{gathered}`

Hence, the proportion for statement A is -30:-25=12:10, and the proportion for statement B is 6.25:1=187.50:30