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 [tex]\frac{1}{2}[/tex].
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.
⇒ [tex]\frac{n}{d}= \frac{3}{5}[/tex] – – – – (1)
Do cross multiplication, we get
⇒ 5n = 3d
When the numerator and denominator are decreased by 2, the fraction is equal to [tex]\frac{1}{2}[/tex].
⇒ [tex]\frac{n-2}{d-2}= \frac{1}{2}[/tex]
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.
Answer:
5n = 3d and 2n – 4 = d – 2 is the answer
Step-by-step explanation:
