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.
1 answer:
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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