Chapter 3: Q5. (page 208)

Suppose yvaries directly as x and $y = 14$ when $x = 4$ . What is the value of y when $x = 9$ ?
A 25.5
B 27.5
C 29.5
D 31.5

Short Answer

Expert verified

The value of y is 31.5 .Option D is correct.

Step by step solution

Step 1. State the concept of Direct Proportionality.

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. The proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is " $\propto$ ".

Here yvaries directly as x.

That is, $y \propto x$

Therefore $y = k x$ … (1)

where kis a constant.

Step 2. Find the value of Constant ‘k’.

Find the value of k by substituting $y = 14 and x = 4$ in equation $y = k x$ .

$\begin{matrix} 14 = k . (4) \\ \frac{14}{4} = \frac{4 k}{4} \\ \frac{7}{2} = k \\ k = \frac{7}{2} \end{matrix}$

Step 3. Calculate the value of ‘y’.

Calculate the value of y by substituting $x = 9 and y = \frac{7}{2}$ in $y = k x$ .

$\begin{matrix} y = \frac{7}{2} \times 9 \\ y = \frac{63}{2} \\ y = 31.5 \end{matrix}$

Thus the value of yis 31.5.

Hence option D is correct.

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Suppose yvaries directly as x and $y = 14$ when $x = 4$ . What is the value of y when $x = 9$ ?
A 25.5
B 27.5
C 29.5
D 31.5

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of Constant ‘k’.

Step 3. Calculate the value of ‘y’.

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Suppose yvaries directly as x and y=14when x=4. What is the value of y when x=9?A 25.5B 27.5C 29.5D 31.5

Short Answer

Step by step solution

Step 1. State the concept of Direct Proportionality.

Step 2. Find the value of Constant ‘k’.

Step 3. Calculate the value of ‘y’.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Discrete Mathematics

Logic and Functions

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Suppose yvaries directly as x and $y = 14$ when $x = 4$ . What is the value of y when $x = 9$ ?
A 25.5
B 27.5
C 29.5
D 31.5