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Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q = 7


Question

Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q = 7

Options

A) 4

B) 3

C) -3

D) -4

The correct answer is A.

Explanation:

\(\frac{1}{4}\)p + 3p = 10...(1)

2p - \(\frac{1}{3}\)q = 7...(2)

Multiply equation (2) by 3 to clear fraction

3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7

6p - q = 21

6p - 21 = q....(3)

substituting 6p - 21 for q in (1)

\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)

Multiply equation (4) by 4 to clear fraction

4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10

p + 12(6p - 21) = 40

p + 72p - 252

73p = 292

p = \(\frac{292}{73}\)

= 4


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Dicussion (1)

  • \(\frac{1}{4}\)p + 3p = 10...(1)

    2p - \(\frac{1}{3}\)q = 7...(2)

    Multiply equation (2) by 3 to clear fraction

    3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7

    6p - q = 21

    6p - 21 = q....(3)

    substituting 6p - 21 for q in (1)

    \(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)

    Multiply equation (4) by 4 to clear fraction

    4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10

    p + 12(6p - 21) = 40

    p + 72p - 252

    73p = 292

    p = \(\frac{292}{73}\)

    = 4

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