Question

examine the worked example. then, answer each question.
amia works as a veterinary assistant at a local animal clinic. yesterday, she helped treat 25 animals, and she was drooled on by 68% of them. how many animals at the clinic drooled on amia yesterday?
rewrite the percent as a decimal and complete the equation.
(□)(□ total animals) = □ animals that drooled
rewrite the percent as a fraction and complete the equation.
(□/100)(□ total animals) = □ animals that drooled
set up a proportion and use n for the unknown. then solve using equivalent ratios.
□/100 = □ animals that drooled / □ total animals

Explanation:

Step1: Convert percentage to decimal

To convert \(68\%\) to a decimal, we divide by \(100\). So \(68\%=0.68\).
The equation \((\text{decimal})(\text{total animals})=\text{animals that drooled}\) becomes \((0.68)(25)\).

Step2: Calculate the product

\(0.68\times25=(0.6 + 0.08)\times25=0.6\times25+0.08\times25 = 15+2=17\)

For the fraction part:

Step1: Convert percentage to fraction

\(68\%=\frac{68}{100}\). The equation \((\frac{\text{numerator}}{100})(\text{total animals})=\text{animals that drooled}\) becomes \((\frac{68}{100})(25)\)

Step2: Calculate the product

\(\frac{68}{100}\times25=\frac{68\times25}{100}=\frac{1700}{100}=17\)

For the proportion part:

Step1: Set up the proportion

The proportion is \(\frac{68}{100}=\frac{n}{25}\) (where \(n\) is the number of animals that drooled)

Step2: Cross - multiply

\(100n=68\times25\)
\(100n = 1700\)

Step3: Solve for \(n\)

\(n=\frac{1700}{100}=17\)

Answer:

• Decimal equation: \((0.68)(25) = 17\)
• Fraction equation: \((\frac{68}{100})(25)=17\)
• Proportion: \(\frac{68}{100}=\frac{17}{25}\)