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
Answers
Step-by-step explanation:
You probably missed that when the numerator and denominator are both decreased by 2, the new fraction is now equal to 1/2.
The numerator of the fraction is "n" and the denominator of the fractions is "d". Initially the numerator and denominator are in the ratio 3 to 5. In equation form we can state this as:
\begin{gathered}n:d=3:5 \\ \\ \frac{n}{d}= \frac{3}{5} \\ \\ 5n=3d\end{gathered}
n:d=3:5dn
= 53
5n=3d
When both numerator and denominator are decreased by 2, the new numerator will be n-2 and denominator will be d-2. These numerator and denominators are in ratio 1 to 2. In equation form we can write this as:
\begin{gathered}n-2:d-2=1:2 \\ \\ \frac{n-2}{d-2} = \frac{1}{2} \\ \\ 2(n-2)=1(d-2) \\ \\ 2n-4=d-2\end{gathered}
n−2:d−2=1:2
d−2
n−2
= 21
2(n−2)=1(d−2)
2n−4=d−2
This is our second equation. Thus the two equation which can be used to solve the problem are:
5n = 3d
and
2n - 4 = d - 2
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