Question

Akira's uncle is about to open a car dealership. His property can accommodate a total inventory of 264 vehicles. The auto manufacturer told him that he should have five times as many cars as trucks. How many trucks should he order?

Answer 1

well, he has room for a total of 264 vehicles, he needs to have "five times as many cars as trucks", namely the cars : trucks ratio must be 5 to 1 or 5:1.

well, to change the total value to a ratio, we simply divide the total amount by the sum of the ratios, namely 264 ÷ (5+1), and distribute accordingly.

$\bf \cfrac{cars}{trucks}\qquad 5:1\qquad \cfrac{5}{1}\qquad \qquad \cfrac{5\cdot \frac{264}{5+1}}{1\cdot \frac{264}{5+1}}\implies \cfrac{5\cdot 44}{1\cdot 44}\implies \cfrac{\stackrel{cars}{220}}{\underset{trucks}{44}}$