“Three chocolate cakes requires 9/4 cups of cocoa powder. Twelve cups of cocoa powder is enough for how many chocolate cakes?”
While the multiplying and dividing of fractions can be tricky, this problem is a simple ratio. Cakes divided by cocoa equals cakes divided by cocoa. Cross multiply and solve for your variable. This is called direct variation – y increases as x increases, and y decreases as x decreases. Since this concept is learned early in one’s academic career, and is even used often in day-to-day life, many students confuse problems of inverse variation (situations in which y increases as x decreases, and vice versa) with the more common direct variation.
“It takes eight men 15 hours to build a shed. How long would it take 12 men to build a shed?” Muscle memory tells you men divided by hours equals men divided by hours, but on second thought, increased manpower would actually decrease the amount of time spent on a project. Where the formula for direct variation is y/h = x/k, the formula for inverse variation is yh = xk, or in this case, man times hours equals man times hours.
Think logically before you begin these problems. Are x and y moving in the same direction, or in opposite directions? Then, choose the appropriate formula.
If you solved the above problems, the correct answers are 16 and 10, respectively.