Please help me solve this:
I can buy fruits in bundles like this: Bundle A: 10 oranges (10%), 80 bananas (80%) and 10 apples (10%) Bundle B: 50 oranges (50%), 40 bananas (40%) and 10 apples (10%) Bundle C: 100 oranges (100%),
I already bought 4 "Bundle A", 4 "Bundle B" and 2 "Bundle C". Which brings me a total of 440 oranges, 480 bananas and 80 apples. Respectively, those represent 44%, 48% and 8% of all the fruits that I currently have.
What formula determines how many of "Bundle B" I must buy so that I reach the closest ratio of 50% in bananas after I purchase it?
Any explanation on the methods used is much appreciated.
Let's say that you buy $x$ bundles of $B$, then the ratio of oranges, bananas and apples is $$440+50x:480+40x:80+10x$$ The total number of fruit is $1000+100x$ so the percentage of bananas held is then $$\frac{480+40x}{1000+100x}\times 100$$ If you want this to be equal to $50$% then we can write $$\frac{480+40x}{1000+100x}\times 100=50$$ $$\frac{480+40x}{1000+100x}=\frac12$$ $$480+40x=\frac12\left(1000+100x\right)$$ $$480+40x=500+50x$$ $$10x=-20$$ $$x=-2$$ But as $x\ge0$ we must buy none of bundle $B$ in order for $x$ to be closest to $-2$ and the ratio be closest to $50$%.