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

Fraction is
`(12)/(17)`

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

`(4)/(5)y=(1)/(3)x`

Solve for y

Multiply both sides by 5/4

`y=(5)/(4) * (1)/(3)x`

`y=(5)/(12)x`

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

Total number of pens =
`x + (5)/(12)x`

Take LCD 12

`(12x)/(12) + (5x)/(12)`

Now add the numerators

`(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

`(x)/((17)/(12)x)`

we cancel out x at the top and bottom

`(1)/((17)/(12))`

Take reciprocal of 17/12 and multiply with top 1

So answer is 12/ 17