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JAMB Mathematics 2024 Paper

Question : 7

Total: 50

If p * q = 2p + pq + q, find p when ( p * 2) - (p * 1) = 40

Solution:

Concept:

The symbol

*

defines a special operation. To find

p

, substitute the second number into

q

in the formula

p \ast q = 2p + pq + q

Explanation:

First compute

p \ast 2

by putting

q = 2

p \ast 2 = 2p + p(2) + 2 = 4p + 2

Next compute

p \ast 1

by putting

q = 1

p \ast 1 = 2p + p(1) + 1 = 3p + 1

Substitute both results into the given equation:

(p \ast 2) - (p \ast 1) = 40

(4p + 2) - (3p + 1) = 40

Simplify the left side:

4p + 2 - 3p - 1 = 40

p + 1 = 40

Subtract

1

from both sides:

p = 39

This matches option A.

Answer:

p = 39

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