Question

Alex mixes 2/3 pounds of walnuts with 3/5 pound of dried fruit. To create more of the same mixture, how many pounds of walnuts does Alex need to mix with one pound of dried fruit?

Answer 1

ANSWER

Alex needs to mix one pound of dried fruit with
$1 \frac{1}{9}$
pounds of walnuts.

EXPLANATION

It was given that, Alex mixes
$\frac{2}{3}$
pounds of walnuts with

$\frac{3}{5}$
pounds of dried fruit.


We can write the ratio,

$\frac{2}{3} : \frac{3}{5}$

Let
$x$
represent how many pounds of walnuts Alex needs to mix with one pound of dried fruit.


Then we can again write the ratio,

$x: 1$
We can therefore write the proportion,


$\frac{2}{3} : \frac{3}{5} = x: 1$

This can be rewritten as,

$\frac{ \frac{2}{3} }{ \frac{3}{5} } = \frac{x}{1}$

We solve for x to obtain,

$\frac{2}{3} \times \frac{5}{3} = x$


This implies that,

$x = \frac{10}{9}$

$x = 1 \frac{1}{9}$

Hence Alex needs to mix
$1\frac{1}{9}$
pounds of walnuts with one pound of dried fruit.