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. 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

The systems of equations that could be used to solve the problem is

5n = 3d

5n = 3d3d + 5n = 4

Given:

numerator = n

denominator = d

Ratio = 3 : 5

Equation 1

n / d = 3/5

cross product

n × 5 = d × 3

5n = 3d

Equation 2

(n + 2) / (d + 2) = 3/5

cross product

(n + 2) 5 = (d + 2)3

5n + 10 = 3d + 6

collect like terms

10 - 6 = 3d - 5n

4 = 3d - 5n

3d + 5n = 4

Therefore, the systems of equations that could be used to solve the problem is

5n = 3d

5n = 3d3d + 5n = 4

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