High School

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Solve for [tex]y[/tex] in the proportion.

[tex]\begin{array}{l} \frac{45}{y} = \frac{27}{30} \\ y = \square \end{array}[/tex]

Answer :

To solve the proportion [tex]\(\frac{45}{y} = \frac{27}{30}\)[/tex] for [tex]\(y\)[/tex], we can use cross-multiplication. Here's a step-by-step explanation:

1. Set up the equation for cross-multiplication:
The proportion [tex]\(\frac{45}{y} = \frac{27}{30}\)[/tex] can be solved by multiplying the numerator of one fraction by the denominator of the other fraction. This gives us:
[tex]\[
45 \times 30 = 27 \times y
\][/tex]

2. Perform the multiplication on the left side:
Calculate the product of 45 and 30:
[tex]\[
45 \times 30 = 1350
\][/tex]

3. Write the equation with the result from step 2:
Substitute the result for the left side:
[tex]\[
1350 = 27 \times y
\][/tex]

4. Solve for [tex]\(y\)[/tex] by dividing both sides by 27:
To isolate [tex]\(y\)[/tex], divide each side of the equation by 27:
[tex]\[
y = \frac{1350}{27}
\][/tex]

5. Calculate the value of [tex]\(y\)[/tex]:
Perform the division:
[tex]\[
y = 50
\][/tex]

Thus, the solution for [tex]\(y\)[/tex] is [tex]\(y = 50\)[/tex].

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