Question

4/5 of Sarah's pens are equal to 1/3 of Matt's pens. Express the number of Matt's pens as a fraction of the total number of pens he and Sarah have.

Answer 1

Answer:

Fraction is $\frac{12}{17}$

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

$\frac{4}{5}y=\frac{1}{3}x$

Solve for y

Multiply both sides by 5/4

$y=\frac{5}{4} * \frac{1}{3}x$

$y=\frac{5}{12}x$

Total number of Matt's and Sarah's pen = x+y

Total number of pens = $x + \frac{5}{12}x$

Take LCD 12

$\frac{12x}{12} + \frac{5x}{12}$

Now add the numerators

$\frac{17x}{12}$

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

$\frac{x}{\frac{17}{12}x}$

we cancel out x at the top and bottom

$\frac{1}{\frac{17}{12}}$

Take reciprocal of 17/12 and multiply with top 1

So answer is 12/ 17