Question $\begin{array}{c} y \alpha \frac{1}{x} \\ y=k\left(\frac{1}{x}\right)=\frac{k}{x} \end{array}$
Follow these steps to solve an inverse variation problem. - Step 1: Find the constant of proportionality, $k$ . - Step 2: Write out the equation $y=\frac{k}{x}$ . - Step 3: Solve for the missing values.
Example Fill in the missing values, assuming that y is inversely proportional to x (to 2 decimal places). \begin{tabular}{|c|c|c|c|} \hline $x$ & 275 & 589 & $\square$ \\ \hline $y$ & 133 & $\square$ & 374 \\ \hline \end{tabular} HINT

Studdy Solution

STEP 1

1. $y$ is inversely proportional to $x$ , meaning $y \alpha \frac{1}{x}$ .
2. The relationship can be expressed as $y = \frac{k}{x}$ , where $k$ is the constant of proportionality.
3. We need to find the missing values in the table, given that $y$ is inversely proportional to $x$ .

STEP 2

1. Find the constant of proportionality, $k$ .
2. Write out the equation $y = \frac{k}{x}$ .
3. Solve for the missing values in the table.

STEP 3

Find the constant of proportionality, $k$ .
Given $x = 275$ and $y = 133$ , use the equation $y = \frac{k}{x}$ .
$133 = \frac{k}{275}$
To find $k$ , multiply both sides by 275:
$k = 133 \times 275$
Calculate $k$ :
$k = 36575$

STEP 4

Write out the equation $y = \frac{k}{x}$ using the calculated $k$ .
The equation is:
$y = \frac{36575}{x}$

STEP 5

Solve for the missing values in the table.
First, find $y$ when $x = 589$ :
$y = \frac{36575}{589}$
Calculate $y$ :
$y \approx 62.09$
Next, find $x$ when $y = 374$ :
$374 = \frac{36575}{x}$
To find $x$ , multiply both sides by $x$ and then divide by 374:
$x = \frac{36575}{374}$
Calculate $x$ :
$x \approx 97.79$
The completed table is:
$\begin{array}{|c|c|c|c|} \hline x & 275 & 589 & 97.79 \\ \hline y & 133 & 62.09 & 374 \\ \hline \end{array}$

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