# Fuzzy the Fuzzball

Fuzzy the fuzzball was very sad.
Everyone knew if you lost your Fuzz you could no longer be a fuzzball.
Fuzzy went to this friend Frizzy and shared his dilemma.
"Don't worry, Fuzzy," Frizzy said. "You can buy new fuzz in the FuzzyFuzz store."

"How much Fuzz do you need?" the clerk asked.
"Enough to make me fuzzy," Fuzzy said. "I'm a perfect sphere, 2.3456" in diameter."

"We sell three types of Fuzz," said the clerk. "Spartan fuzz is \$2.34 per cm². Standard fuzz is \$3.45 per cm². Super Fuzz is \$4.56 per cm²." "Ok," said Fuzzy. "I have \$543.21. I will spend up to 67% of my money to buy the best Fuzz I can afford. I sure hope I can afford to become Super Fuzzy!"

How fuzzy is Fuzzy the fuzzball after his purchase?

• Dollar signs are used for math formatting. You have to escape them with a backslash (\\\$to get a dollar sign). – f'' Feb 29, 2016 at 23:57 • ^vote for creatively dressing a linear-programming puzzle that clearly is not a homework problem, assuming that Fuzzy's goal is to completely refuzz, just as Super-bly as possible – humn Mar 1, 2016 at 0:30 • Is the fuzz sold in units of a particular size, or can we assume that it's infinitely divisible? Mar 1, 2016 at 5:32 • @jpmc26 It seems that they can divide the fuzz into any size, though the price is given per cm2. Mar 1, 2016 at 15:33 ## 2 Answers So Fuzzy's total surface area is $$17.28$$ Then we multiply that by $$2.54^2$$ to get cm. $$111.483648$$ We now find 67% of 543.21 363.9507 Now we divide the money into parts. How many $$cm^2$$ total for each? Super: 79.91375 cm$$^2$$ for \$363.9507
Regular: 105.49
Spartan: 155.53

So,

since only one of them is obviously greater, we can say he can be completely covered in Spartan Fuzz.

Fuzzy's:
EDIT: Thanks to @bleh

2.3456 inches in diameter
Which is $\approx 2.9789cm$ in radius
For an total surface area of $4 \pi 2.9789^2 \approx 111.51cm^2$
He has $67\%$ of $\$543.21$to spend so can afford$\frac{67}{100} *\frac{\$543.21}{111.51cm^2}\approx \$3.26/cm^2$Spartan fuzz is$ \$2.34/cm^2$.
Standard fuzz is $\$3.45/cm^2 $Super Fuzz costs$ \$4.56/cm^2$
So, Can we mix a bit of Spartan with Standard?

• He wants to use only 67%.
– bleh
Mar 1, 2016 at 1:08