**Question:**

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

**Answer:**

5n = 3d and 2n – 4 = d – 2

**Solution:**

Let **n** be the numerator of the fraction and **d** be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ – – – – (1)

Do cross multiplication, we get

⇒ **5n = 3d**

When the numerator and denominator are decreased by 2, the fraction is equal to .

⇒

Do cross multiplication, we get

⇒ 2(n –2)=1(d – 2)

⇒ **2n – 4 = d – 2**

**Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.**