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reversing its digits is
9. The numerator of a fraction is five less than the
denominator. Also, four times the numerator is one
more than the denominator. Find the fraction.
(A) 4/9
(B) 3/8
(C) 2/7
(D) 7/12
- The denominator of a fraction is two more than its

Verified Answer :

GinnyAnswer

To find the fraction, we'll let the numerator be denoted as \(\( n \)\) and the denominator be denoted as \(\( d \)\). Given the information:

1. The numerator \(\( n \)\) is five less than the denominator \(\( d \)\). This can be expressed as:
\(\[ n = d - 5 \]\) (Equation 1)

2. Four times the numerator is one more than the denominator. This relationship can be written as:
\(\[ 4n = d + 1 \]\) (Equation 2)

We want to find the values of \(\( n \)\) and \(\( d \)\) that satisfy both equations. We'll start with Equation 1 and use it to express \(\( n \)\) in terms of \(\( d \)\).

Substitute \(\( n \)\) into Equation 2:
\(\[ 4(d - 5) = d + 1 \]\)
Expanding and simplifying:
\(\[ 4d - 20 = d + 1 \]\)
Combine like terms to isolate \(\( d \)\):
\(\[ 4d - d = 1 + 20 \]\)
\(\[ 3d = 21 \]\)
Divide both sides by 3 to solve for \(\( d \)\):
\(\[ d = \frac{21}{3} \]\)
\(\[ d = 7 \]\)

Now we have the value of the denominator. Using Equation 1, we find the numerator:
\(\[ n = d - 5 \]\)
Substitute the value of \(\( d \)\):
\(\[ n = 7 - 5 \]\)
\(\[ n = 2 \]\)

So, we found out that the numerator \(\( n \)\) is 2 and the denominator \(\( d \)\) is 7. Therefore, the fraction is \(\( \frac{2}{7} \)\), which corresponds to option (C) \(\( \frac{2}{7} \)\).

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