Answer:
Fraction is [tex]\frac{12}{17}[/tex]
Step-by-step explanation:
Let x be the number of Matt's pen
and y be the number of Sarah's pen
4/5 of Sarah's pen (y) = 1/3 of Matt's pen (x)
So equation becomes
[tex]\frac{4}{5}y=\frac{1}{3}x[/tex]
Solve for y
Multiply both sides by 5/4
[tex]y=\frac{5}{4} * \frac{1}{3}x[/tex]
[tex]y=\frac{5}{12}x[/tex]
Total number of Matt's and Sarah's pen = x+y
Total number of pens = [tex]x + \frac{5}{12}x[/tex]
Take LCD 12
[tex]\frac{12x}{12} + \frac{5x}{12}[/tex]
Now add the numerators
[tex]\frac{17x}{12}[/tex]
To express the number of Matts pens as a fraction
We divide the number of Matt's pen 'x' by the total number of pens
[tex]\frac{x}{\frac{17}{12}x}[/tex]
we cancel out x at the top and bottom
[tex]\frac{1}{\frac{17}{12}}[/tex]
Take reciprocal of 17/12 and multiply with top 1
So answer is 12/ 17
