# calculate proportion of salt and sand

suppose that we have following question:

there is two mixture of salt and sand,in the first the proportion of salt to sand is $2:1$ and in second mixture $1:4$;if we take equal quantities of both mixture,we are interested what would be ration of salt and sand in new mixture?

my attempt is following,let us take quantity $x$ from both mixture,then in total we will have $2*x$; in each part when we take from two mixture ,proportion is following;

in the first half the amount of salt is $2x/3$ and sand is $x/3$;

in the second half we have $x/5$ salt and $4*x/5$;

now if we add we will get salt is $13*x/5$ and sand is $21*x/20$;

the proportion is $52/63$; is it correct? In the answer it says $13:17$. Please help me see what is wrong with my calculation.

• Make up your mind whether it is sugar or sand which is mixed with the salt! Commented Jul 31, 2013 at 7:09
• i have updated sorry Commented Jul 31, 2013 at 7:10

You added the fractions incorrectly. The total amount of salt is $\frac23x+\frac15x=\frac{13}{15}x$, not $\frac{13}5x$, and the total amount of sand is $\frac13x+\frac45x=\frac{17}{15}x$, not $\frac{21}{20}x$, so the ratio is

$$\frac{\frac{13}{15}x}{\frac{17}{15}x}=\frac{13}{17}\;.$$

• i see my typo,thanks very much Commented Jul 31, 2013 at 7:19
• @dato: You’re very welcome. Commented Jul 31, 2013 at 7:20

Let's call the quantity of the final mixture $30u$ - I got 30 because I wanted half the mixture to be easily divisible into $3=2+1$ units and also $5=1+4$ units.

In the first half $(15u)$ we have $10u$ salt and $5u$ sand.

In the second half we have $3u$ salt and $12u$ sand.

This makes $13u$ salt and $17u$ sand.

You seem to have added the fractions incorrectly - $$\frac {2x}3+\frac x5=\frac {13x}{15}$$$$\frac x3+\frac {4x}5=\frac {17x}{15}$$