Answer :
To solve the problem where [tex]\( x \)[/tex] varies directly as [tex]\( y \)[/tex], we follow these steps:
1. Understand Direct Variation: If [tex]\( x \)[/tex] varies directly as [tex]\( y \)[/tex], it means there is a constant [tex]\( k \)[/tex] such that [tex]\( x = ky \)[/tex].
2. Find the Constant [tex]\( k \)[/tex]:
We are given that [tex]\( x = 7.5 \)[/tex] when [tex]\( y = 10 \)[/tex]. Using the direct variation equation:
[tex]\[
7.5 = k \times 10
\][/tex]
To find [tex]\( k \)[/tex], divide both sides by 10:
[tex]\[
k = \frac{7.5}{10} = 0.75
\][/tex]
3. Use the Constant to Find the New Value of [tex]\( x \)[/tex]:
We need to find [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex]. Substitute the values into the direct variation equation:
[tex]\[
x = 0.75 \times 4
\][/tex]
4. Calculate [tex]\( x \)[/tex]:
[tex]\[
x = 3.0
\][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( 3 \)[/tex].
1. Understand Direct Variation: If [tex]\( x \)[/tex] varies directly as [tex]\( y \)[/tex], it means there is a constant [tex]\( k \)[/tex] such that [tex]\( x = ky \)[/tex].
2. Find the Constant [tex]\( k \)[/tex]:
We are given that [tex]\( x = 7.5 \)[/tex] when [tex]\( y = 10 \)[/tex]. Using the direct variation equation:
[tex]\[
7.5 = k \times 10
\][/tex]
To find [tex]\( k \)[/tex], divide both sides by 10:
[tex]\[
k = \frac{7.5}{10} = 0.75
\][/tex]
3. Use the Constant to Find the New Value of [tex]\( x \)[/tex]:
We need to find [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex]. Substitute the values into the direct variation equation:
[tex]\[
x = 0.75 \times 4
\][/tex]
4. Calculate [tex]\( x \)[/tex]:
[tex]\[
x = 3.0
\][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( 3 \)[/tex].
