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Answer :
To solve this problem, we need to follow these steps:
1. Understand what it means for [tex]\( y \)[/tex] to be inversely proportional to [tex]\( x \)[/tex]. This means there exists a constant [tex]\( k \)[/tex] such that:
[tex]\[
y = \frac{k}{x}
\][/tex]
2. Use the given values ([tex]\( y = 7.5 \)[/tex] and [tex]\( x = 8 \)[/tex]) to find the constant [tex]\( k \)[/tex].
3. Use the constant [tex]\( k \)[/tex] and the new value of [tex]\( y \)[/tex] to find the new value of [tex]\( x \)[/tex].
Let's go through the steps:
### Step 1: Set up the relationship
Since [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex]:
[tex]\[
y = \frac{k}{x}
\][/tex]
### Step 2: Find the constant [tex]\( k \)[/tex]
Given that when [tex]\( y = 7.5 \)[/tex], [tex]\( x = 8 \)[/tex]:
[tex]\[
7.5 = \frac{k}{8}
\][/tex]
To find [tex]\( k \)[/tex], multiply both sides by 8:
[tex]\[
k = 7.5 \times 8 = 60
\][/tex]
### Step 3: Use the constant [tex]\( k \)[/tex] to find the new value of [tex]\( x \)[/tex]
We need to find [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex]:
[tex]\[
y = \frac{k}{x}
\][/tex]
Substitute [tex]\( y = 5 \)[/tex] and [tex]\( k = 60 \)[/tex]:
[tex]\[
5 = \frac{60}{x}
\][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by [tex]\( x \)[/tex]:
[tex]\[
5x = 60
\][/tex]
Then divide both sides by 5:
[tex]\[
x = \frac{60}{5} = 12
\][/tex]
So, when [tex]\( y = 5 \)[/tex], [tex]\( x = 12 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex] is [tex]\( 12 \)[/tex].
1. Understand what it means for [tex]\( y \)[/tex] to be inversely proportional to [tex]\( x \)[/tex]. This means there exists a constant [tex]\( k \)[/tex] such that:
[tex]\[
y = \frac{k}{x}
\][/tex]
2. Use the given values ([tex]\( y = 7.5 \)[/tex] and [tex]\( x = 8 \)[/tex]) to find the constant [tex]\( k \)[/tex].
3. Use the constant [tex]\( k \)[/tex] and the new value of [tex]\( y \)[/tex] to find the new value of [tex]\( x \)[/tex].
Let's go through the steps:
### Step 1: Set up the relationship
Since [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex]:
[tex]\[
y = \frac{k}{x}
\][/tex]
### Step 2: Find the constant [tex]\( k \)[/tex]
Given that when [tex]\( y = 7.5 \)[/tex], [tex]\( x = 8 \)[/tex]:
[tex]\[
7.5 = \frac{k}{8}
\][/tex]
To find [tex]\( k \)[/tex], multiply both sides by 8:
[tex]\[
k = 7.5 \times 8 = 60
\][/tex]
### Step 3: Use the constant [tex]\( k \)[/tex] to find the new value of [tex]\( x \)[/tex]
We need to find [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex]:
[tex]\[
y = \frac{k}{x}
\][/tex]
Substitute [tex]\( y = 5 \)[/tex] and [tex]\( k = 60 \)[/tex]:
[tex]\[
5 = \frac{60}{x}
\][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by [tex]\( x \)[/tex]:
[tex]\[
5x = 60
\][/tex]
Then divide both sides by 5:
[tex]\[
x = \frac{60}{5} = 12
\][/tex]
So, when [tex]\( y = 5 \)[/tex], [tex]\( x = 12 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex] is [tex]\( 12 \)[/tex].
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