Question

You wonder how many cars there are in your area. You call up the Ford dealership and ask how many Fords they’ve sold. They report that they’ve sold a total of 15,000 cars. You then take a lawn chair and camp out on a busy road and count cars. You count 1200 cars and note that 700 of them are Fords. Estimate the number of cars in your area.

Answer 1

if we take 1200 as the 100%, how much percentage is 700 of it?

well
`\bf \begin{array}{ccllll} amount&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1200&100\\ 700&x \end{array}\implies \cfrac{1200}{700}=\cfrac{100}{x}\implies x=\cfrac{700\cdot 100}{1200} \\\\\\ x=\cfrac{175}{3}`

so, (175/3)% or roughly 58.3%

now, how much is (175/3)% of 15000 ?
well, if we take 15000 as the 100%
then
`\bf \begin{array}{ccllll} amount&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 15000&100\\ x&(175)/(3) \end{array}\implies \cfrac{15000}{x}=\cfrac{100}{(175)/(3)} \\\\\\ \cfrac{15000\cdot (175)/(3)}{100}=x\implies \cfrac{5000\cdot 175}{100}=x`