Question

Rosa earns $12 per hour. In 7.5 hours, she will earn x dollars. Which is a valid proportion that can be used to solve the problem?

Answer 1

`\bf \begin{array}{ccllll} dollars&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 12&1\\ x&7.5 \end{array}\implies \cfrac{12}{x}=\cfrac{1}{7.5}`

Answer 2

`\frac{\$12}{\text{1 hour}}=\frac{\$x}{\text{7.5 hour}}`

`x=\$90`

Explanation:

We have been given that Rosa earns $12 per hour. We can represent this information as:

`\frac{\$12}{\text{1 hour}}`

We are also told that in 7.5 hours, she will earn x dollars. We can represent this information as:

`\frac{x}{\text{7.5 hour}}`

Since proportion states that two quantities are equal, so we can set a proportion for our given quantities as:

`\frac{\$12}{\text{1 hour}}=\frac{x}{\text{7.5 hour}}`

Therefore, the proportion
`\frac{\$12}{\text{1 hour}}=\frac{\$x}{\text{7.5 hour}}` can be used to solve the problem.

Let us solve for x.

`\frac{\$12}{\text{1 hour}}*\text{7.5 hour}=\frac{x}{\text{7.5 hour}}*\text{7.5 hour}`

`\$12*7.5=x`

`\$90=x`

Therefore, the value of x is $90.