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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

A) 4

B) 3

C) -3

D) -4

### 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

## 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