A quantity P varies partially as x and partially as the square of y. When x = 2 and y = 3,… — JAMB UTME

A quantity $P$ varies partially as $x$ and partially as the square of $y$ . When $x = 2$ and $y = 3$ , $P = 24$ , and when $x = 5$ and $y = 1$ , $P = 17$ . What is the value of $P$ when $x = 4$ and $y = 3$ ?

30Answer
B
35
C
26
D
21

Answer

The value of

P

is 30.

The relationship follows the partial variation formula

P = k_1 x + k_2 y^2

. Substituting the given conditions gives

2k_1 + 9k_2 = 24

and

5k_1 + k_2 = 17

. Solving these simultaneous equations yields

k_1 = 3

and

k_2 = 2

. Evaluating

P = 3(4) + 2(3^2)

produces

12 + 18 = 30

Step-by-Step Solution

Set up the general formula for partial variation.

P = k_1 x + k_2 y^2

, where

k_1

and

k_2

are constants.

Partial variation combines terms linearly with separate variation constants.

Substitute the given pairs of values to form simultaneous linear equations.

Equation (1):

2k_1 + 9k_2 = 24

; Equation (2):

5k_1 + k_2 = 17

Plugging in

(x=2, y=3, P=24)

and

(x=5, y=1, P=17)

creates a system of equations in terms of

k_1

and

k_2

Solve the simultaneous linear equations for

k_1

and

k_2

From Equation (2),

k_2 = 17 - 5k_1

. Substitute into Equation (1):

2k_1 + 9(17 - 5k_1) = 24 \implies -43k_1 = -129 \implies k_1 = 3

. Then

k_2 = 17 - 5(3) = 2

Finding the specific values of the variation constants is required to complete the formula.

Calculate

P

for

x = 4

and

y = 3

using the complete formula

P = 3x + 2y^2

P = 3(4) + 2(3^2) = 12 + 2(9) = 12 + 18 = 30

Evaluating the relationship with the target parameters produces the final answer.

Key Concept

Partial Variation and Simultaneous Linear Equations

Estimated Time:2m 0s

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