Question

1. if \\(x_1 = 45\\), \\(x_2 = 0.5\\), and \\(y_2 = 2\\), determine the value of \\(y_1\\).
2. if \\(x_1 = \\$11.00\\), \\(y_1 = 2\\), and \\(y_2 = 3\\), determine the value of \\(x_2\\).
3. if \\(y_1 = 560\\), \\(x_2 = 5\\), and \\(y_2 = 100\\), determine the value of \\(x_1\\).
4. if \\(x_1 = 1\\), \\(y_1 = 120\\), and \\(x_2 = 1.75\\), determine the value of \\(y_2\\).

Explanation:

Set up proportion equations

Assuming direct variation/proportionality of the form \(\frac{x_1}{y_1} = \frac{x_2}{y_2}\):

$$ \frac{x_1}{y_1} = \frac{x_2}{y_2} \implies x_1 y_2 = x_2 y_1 $$

Solve for the unknowns

For Question 5:

$$ \frac{45}{y_1} = \frac{0.5}{2} \implies 0.5 y_1 = 90 \implies y_1 = 180 $$

For Question 6:

$$ \frac{11.00}{2} = \frac{x_2}{3} \implies 2 x_2 = 33.00 \implies x_2 = \$16.50 $$

For Question 7:

$$ \frac{x_1}{560} = \frac{5}{100} \implies 100 x_1 = 2800 \implies x_1 = 28 $$

For Question 8:

$$ \frac{1}{120} = \frac{1.75}{y_2} \implies y_2 = 120 \times 1.75 \implies y_2 = 210 $$

Answer:

No.	Answer
6	\(x_2 = \$16.50\)
7	\(x_1 = 28\)
8	\(y_2 = 210\)