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Find the value of [tex]y[/tex] if [tex]\frac{5}{6} = \frac{y}{72}[/tex].

Find the value of [tex]x[/tex] if [tex]x + x_5 = \frac{32}{40}[/tex].

Answer :

Sure, let's solve the problems step-by-step.

1. Finding the value of [tex]$y$[/tex]:

We have the equation:
[tex]\[
\frac{5}{6} = \frac{y}{72}
\][/tex]

To solve for [tex]$y$[/tex], we can use cross-multiplication. This means we multiply the numerator of one fraction by the denominator of the other fraction. So, we get:

[tex]\[
5 \times 72 = 6 \times y
\][/tex]

Calculating the left side:
[tex]\[
5 \times 72 = 360
\][/tex]

Now we have:
[tex]\[
360 = 6 \times y
\][/tex]

To solve for [tex]$y$[/tex], divide both sides by 6:
[tex]\[
y = \frac{360}{6}
\][/tex]

So, the value of [tex]$y$[/tex] is 60.

2. Finding the value of [tex]$x + x_5$[/tex]:

We start with the equation:
[tex]\[
x + x_5 = \frac{32}{40}
\][/tex]

First, simplify the fraction [tex]$\frac{32}{40}$[/tex]. We do this by finding the greatest common divisor (GCD) of 32 and 40, which is 8. So, divide both the numerator and the denominator by 8:

[tex]\[
\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]

Now, convert the fraction to a decimal to find that [tex]$x + x_5 = 0.8$[/tex].

In conclusion, the value of [tex]$y$[/tex] is 60, and the value of [tex]$x + x_5$[/tex] is 0.8.

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