Question

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

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 3n + 6 = 2d + 4
5n = 3d and 4n + 4 = 3d + 6
3n = 5d and 3n + 6 = 2d + 4

Answer 1

3n=5d and 3n = 5d and 3n + 6 = 2d + 4

Explanation:

Answer 2

Answer: The correct option is

(A)
`5n=3d~~~\textup{and}~~~3n+6=2d+4.`

Step-by-step explanation: Given that the numerator and denominator of a fraction are in the ratio of 3 to 5. When the numerator and denominator are both increased by 2, the fraction is equal to \dfrac{2}{3}.

We are to select the system of equations that could be used to solve the problem.

Since n denotes the numerator and m denotes the denominator of the given fraction, so we have

`(n)/(d)=(3)/(5)\\\\\\\Rightarrow 5n=3d,`

and

`(n+2)/(d+2)=(2)/(3)\\\\\\\Rightarrow 3(n+2)=2(d+2)\\\\\Rightarrow 3n+6=2d+4.`

Thus, the required system of equations is

`5n=3d~~~\textup{and}~~~3n+6=2d+4.`

Option (A) is CORRECT.