Question

if the numerator of a fraction is increased by 1, it's value becomes ¾. If the denominator is increased by 2, it's value becomes ½. Find the original fraction.(solve using two variables)​

Answer 1

Answer:

x=5 and y=8

Step-by-step explanation:

Case I:

(x + 1)÷y = 3/4

Cross-multiplying:

4(x + 1) = 3y

4x + 4 = 3y

x = (3y - 4)÷4 ⇒ Equation 1

Case II:

x÷(y + 2) = 1/2

Cross-multiplying:

2x = y + 2 ⇒ Equation 2

Substituting x = (3y - 4)÷4 in Equation 2

[2(3y - 4)÷4] = y + 2

(3y - 4)÷2 = y + 2

Cross-multiplying

3y - 4 = 2(y + 2)

3y - 4 = 2y + 4

y = 8

x = (3y - 4)÷4

x = (24 - 4)÷4

x = 20/4

x = 5

∴ x = 5 and y = 8