QuestionDetermine if the relationship between workers $x$ and days $y$ to paint 50 apartments is proportional. Explain why.

Studdy Solution

STEP 1

Assumptions1. The number of workers is represented by $x$ . . The duration of the job (in days) is represented by $y$ .
3. The relationship between the number of workers and the duration of the job is given in the table.

STEP 2

To determine if the relationship is proportional, we need to check if the ratio of $x$ to $y$ is constant for all pairs of values in the table.A relationship is proportional if the ratio $\frac{x}{y}$ is constant.

STEP 3

Let's calculate the ratio for each pair of values in the table.
For $x =5$ and $y =60$ , the ratio is $\frac{5}{60}$ .
For $x =10$ and $y =30$ , the ratio is $\frac{10}{30}$ .
For $x =15$ and $y =20$ , the ratio is $\frac{15}{20}$ .
For $x =20$ and $y =15$ , the ratio is $\frac{20}{15}$ .
For $x =25$ and $y =12$ , the ratio is $\frac{25}{12}$ .

STEP 4

Now, let's simplify each ratio to its simplest form.
$\frac{}{60}$ simplifies to $\frac{1}{12}$ .
$\frac{10}{30}$ simplifies to $\frac{1}{3}$ .
$\frac{15}{20}$ simplifies to $\frac{3}{4}$ .
$\frac{20}{15}$ simplifies to $\frac{4}{3}$ .
$\frac{25}{12}$ remains as $\frac{25}{12}$ .

STEP 5

As we can see, the ratios are not constant. They vary for different pairs of values in the table.
Therefore, the relationship between the number of workers and the duration of the job is not proportional.

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