A housewife buys a certain amount of beef at £4 per kilo and the same amount of sausages at £3 per kilo. If she had split the money she spent equally between the beef and sausages she would have got 2 kilos more. How much did she spend
A housewife buys a certain amount of beef at £4 per kilo and the same amount of sausages at £3 per kilo. If she had split the money she spent equally between the beef and sausages she would have got 2 kilos more. How much did she spend
It is worded in a confusing sense but I think I understand it. Let $\displaystyle x$ represent the money she spend on sausages. Also $\displaystyle x$ is the money she spend on beef because she spilt the money equally. Since she can buy more sausages then beef (they are less expensive) the difference between them is 2 (because she gets 2 more kilos). Now place that into an equation. If she spends $\displaystyle x$ yen on sausages then she gets $\displaystyle \frac{x}{3}$kilos because they are worth (3 yen per kilo). Similarily she gets $\displaystyle \frac{x}{4}$ kilos of beef. Thus, their difference is 2:Originally Posted by bonbhoy
$\displaystyle \frac{x}{3}-\frac{x}{4}=2$
To solve this you need to find the common denominator. Which is 12, and multiply both sides by 12:
$\displaystyle 12\frac{x}{3}-12\frac{x}{4}=12\times 2$
thus,
$\displaystyle 4x-3x=24$
thus,
$\displaystyle x=24kg$
Thus, she brought 24 kilos for both of them. Thus, a total of 48 kilograms of meat where brough.
Let $\displaystyle x$ denote the mass of beef bought and $\displaystyle s$ be the amount spent.Originally Posted by bonbhoy
Then:
$\displaystyle 4x+3x=s$
Now if instead $\displaystyle s/2$ is spent on beef and also on sausage these
buy $\displaystyle (s/2)/4\ kg$ of beef and $\displaystyle (s/2)/3\ kg$ of sausage. As the sum
of these is $\displaystyle 2\ kg$ more than previously we have:
$\displaystyle s/8+s/6 = 2x+2$,
but $\displaystyle s=7x$ so:
$\displaystyle \frac{7x}{8}+\frac{7x}{6}=2x+2$,
which has solution $\displaystyle x=48\ kg$, or $\displaystyle s= 336$pounds
These numbers seem implausibly large given the scenario.
RonL