Respuesta :
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
[tex]\begin{gathered} -30\text{ is to -25 as 12 is to 10} \\ -30\colon-25=12\colon10 \\ This\text{ is the breakdown} \\ \frac{-30}{-25}=\frac{30}{25}=\frac{5\times6}{5\times5}=\frac{6}{5} \\ so, \\ -30\colon-25=6\colon5 \\ \text{Also,} \\ 12\colon10=\frac{12}{10}=\frac{2\times6}{2\times5}=\frac{6}{5} \\ so, \\ 12\colon10=6\colon5 \\ \text{Therefore,} \\ -30\colon-25=12\colon10=6\colon5 \\ -30\colon-25=12\colon10 \end{gathered}[/tex]Statement B: $6.25 per hour is proportional to $187.50 per 30 hr. The proportion for this statement is
[tex]\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 \\ \frac{6.25}{1}=\frac{625}{100}=\frac{25\times25}{25\times4}=\frac{25}{4} \\ \text{Also,} \\ 187.50\colon30=\frac{187.50}{30}=\frac{1875}{300}=\frac{75\times25}{75\times4}=\frac{25}{4} \\ \\ \text{Therefore,} \\ 6.25\colon1=187.50\colon30=25\colon4 \\ 6.25\colon1=187.50\colon30 \end{gathered}[/tex]Hence, the proportion for statement A is -30:-25=12:10, and the proportion for statement B is 6.25:1=187.50:30
