Answer:
[tex]\textsf{The fraction is }: \dfrac{5}{12}[/tex]
Step-by-step explanation:
[tex]\textsf{Let the unknown fraction be }\dfrac{a}{b}[/tex]
The fraction becomes 1/3 when 1 is subtracted from the numerator:
[tex]\implies \dfrac{a-1}{b}=\dfrac{1}{3}[/tex]
[tex]\implies 3(a-1)=b[/tex]
[tex]\implies 3a-3=b[/tex]
The fraction becomes 1/4 when 8 is added to its denominator:
[tex]\implies \dfrac{a}{b+8}=\dfrac{1}{4}[/tex]
[tex]\implies 4a=b+8[/tex]
[tex]\implies b=4a-8[/tex]
Solve for [tex]a[/tex] by substitution:
[tex]\implies 3a-3=4a-8[/tex]
[tex]\implies 3a-4a=-8+3[/tex]
[tex]\implies -a=-5[/tex]
[tex]\implies a=5[/tex]
Substitute found value of [tex]a[/tex] into [tex]b=4a-8[/tex] and solve for [tex]b[/tex]:
[tex]\implies b=4(5)-8[/tex]
[tex]\implies b=20-8[/tex]
[tex]\implies b=12[/tex]
[tex]\textsf{Therefore, the fraction is }: \dfrac{5}{12}[/tex]
