A quantity y is partly constant and partly varies directly as x. When x = 2, y = 10, and w… — JAMB UTME

A quantity $y$ is partly constant and partly varies directly as $x$ . When $x = 2$ , $y = 10$ , and when $x = 5$ , $y = 19$ . What is the value of $y$ when $x = 8$ ?

28Answer
B
35
C
40
D
25

Answer

The value of

y

when

x = 8

is 28.

By representing partial variation as

y = c + kx

, substituting the given conditions gives two simultaneous linear equations:

10 = c + 2k

and

19 = c + 5k

. Subtracting the first equation from the second yields

3k = 9

, so

k = 3

. Substituting

k = 3

back into the first equation yields

c = 4

. The general equation is

y = 4 + 3x

. Evaluating at

x = 8

gives

y = 4 + 3(8) = 28

Step-by-Step Solution

Set up the partial variation equation

y = c + kx

, where

c

is the constant part and

k

is the constant of variation.

Partial variation consists of a fixed term plus a variable term.

Substitute given values to form simultaneous equations

Equation 1:

10 = c + 2k

Equation 2:

19 = c + 5k

Two pairs of

(x, y)

values are provided to solve for the two unknown constants

c

and

k

Solve for

k

and

c

Subtract Equation 1 from Equation 2:

9 = 3k \implies k = 3

.
Substitute

k = 3

into Equation 1:

10 = c + 2(3) \implies c = 4

.
Thus,

y = 4 + 3x

Eliminating

c

yields the value of

k

, which is then used to find

c

Calculate

y

for

x = 8

y = 4 + 3(8) = 4 + 24 = 28

Substitute the required value of

x

into the established formula.

Key Concept

Partial Variation and Simultaneous Equations

Question

Answer

Step-by-Step Solution

Key Concept

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