Answer :
Let's solve the given problems step-by-step.
Part 1: Finding the time Mustafa will take to read 180 pages
Mustafa reads 15 pages in 50 minutes. We need to find the time in hours he will take to read a book of 180 pages at the same reading rate.
1. Find the reading rate in terms of pages per minute:
[tex]\[
\text{Reading rate} = \frac{15 \text{ pages}}{50 \text{ minutes}} = 0.3 \text{ pages per minute}
\][/tex]
2. Calculate the total reading time for 180 pages:
[tex]\[
\text{Total time in minutes} = \frac{180 \text{ pages}}{0.3 \text{ pages per minute}} = 600 \text{ minutes}
\][/tex]
3. Convert the total time from minutes to hours:
[tex]\[
\text{Total time in hours} = \frac{600 \text{ minutes}}{60 \text{ minutes per hour}} = 10 \text{ hours}
\][/tex]
So, Mustafa will take 10 hours to read 180 pages.
Part 2: Solving the proportions
1. Solve the proportion [tex]\(\frac{15}{x} = \frac{45}{60}\)[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{15}{x} = \frac{45}{60}
\][/tex]
Simplify the right side:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
Now cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
15 \cdot 4 = 3 \cdot x \implies 60 = 3x \implies x = \frac{60}{3} = 20
\][/tex]
Thus, [tex]\( x = 20 \)[/tex].
2. Solve the proportion [tex]\( \frac{18}{x+2} = \frac{9}{12} \)[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{18}{x+2} = \frac{9}{12}
\][/tex]
Simplify the right side:
[tex]\[
\frac{9}{12} = \frac{3}{4}
\][/tex]
Now cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
18 \cdot 4 = 3 \cdot (x + 2) \implies 72 = 3(x + 2) \implies 72 = 3x + 6 \implies 66 = 3x \implies x = \frac{66}{3} = 22
\][/tex]
Thus, [tex]\( x = 22 \)[/tex].
Summary:
1. Mustafa will take 10 hours to read 180 pages.
2. The solution to the proportion [tex]\(\frac{15}{x} = \frac{45}{60}\)[/tex] is [tex]\( x = 20 \)[/tex].
3. The solution to the proportion [tex]\(\frac{18}{x+2} = \frac{9}{12}\)[/tex] is [tex]\( x = 22 \)[/tex].
Part 1: Finding the time Mustafa will take to read 180 pages
Mustafa reads 15 pages in 50 minutes. We need to find the time in hours he will take to read a book of 180 pages at the same reading rate.
1. Find the reading rate in terms of pages per minute:
[tex]\[
\text{Reading rate} = \frac{15 \text{ pages}}{50 \text{ minutes}} = 0.3 \text{ pages per minute}
\][/tex]
2. Calculate the total reading time for 180 pages:
[tex]\[
\text{Total time in minutes} = \frac{180 \text{ pages}}{0.3 \text{ pages per minute}} = 600 \text{ minutes}
\][/tex]
3. Convert the total time from minutes to hours:
[tex]\[
\text{Total time in hours} = \frac{600 \text{ minutes}}{60 \text{ minutes per hour}} = 10 \text{ hours}
\][/tex]
So, Mustafa will take 10 hours to read 180 pages.
Part 2: Solving the proportions
1. Solve the proportion [tex]\(\frac{15}{x} = \frac{45}{60}\)[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{15}{x} = \frac{45}{60}
\][/tex]
Simplify the right side:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
Now cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
15 \cdot 4 = 3 \cdot x \implies 60 = 3x \implies x = \frac{60}{3} = 20
\][/tex]
Thus, [tex]\( x = 20 \)[/tex].
2. Solve the proportion [tex]\( \frac{18}{x+2} = \frac{9}{12} \)[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{18}{x+2} = \frac{9}{12}
\][/tex]
Simplify the right side:
[tex]\[
\frac{9}{12} = \frac{3}{4}
\][/tex]
Now cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
18 \cdot 4 = 3 \cdot (x + 2) \implies 72 = 3(x + 2) \implies 72 = 3x + 6 \implies 66 = 3x \implies x = \frac{66}{3} = 22
\][/tex]
Thus, [tex]\( x = 22 \)[/tex].
Summary:
1. Mustafa will take 10 hours to read 180 pages.
2. The solution to the proportion [tex]\(\frac{15}{x} = \frac{45}{60}\)[/tex] is [tex]\( x = 20 \)[/tex].
3. The solution to the proportion [tex]\(\frac{18}{x+2} = \frac{9}{12}\)[/tex] is [tex]\( x = 22 \)[/tex].
