Mind Twisting vacation Trip with Proportion

by Juliet Robinsons
(New Zealand)

Danny and Melissa decided to rent a campervan from a motorhome company for their 20-day vacation. They are already up from packing up their stuffs when they remember to bring some condiments. They are having problem on how many kilograms they will have to buy from the supermarket. While on the the grocery store, Melissa saw a mind twisting math problem that is exactly the same on what they need to buy.

The math problem goes like this:

If Four(4) kilograms of Tea is worth Eight(8) kilograms of sugar, Five(5) kilograms of Sugar is worth Twelve(12) kilogram of Flour, Seven(7) kilogram of flour is worth One(1) kilogram of coffee, how many kilograms of tea is worth Twenty-four(24) kilograms of coffee?

Choices
A. 35
B. 24
C. 70
D. None


Answer: ?


If 1 kg of coffee has 7 kg of flour, then 24 kg of coffee has 24 × 7 kg of flour or 168 kg of flour.

24 kg of coffee is equivalent to 168 kg of flour


5 kg of sugar is equivalent to 12 kg of flour

x kg of sugar is equivalent to 168 kg of flour


We can also write the following


5 kg ____________ 12 kg


x kg ____________ 168 kg


Cross multiplication is appropriate here


x × 12 = 5 × 168

12x = 840

x = 840/12

x = 70 kg

70 kg of sugar is equivalent to 168 kg of flour


4 kg of tea is equivalent to 8 kg of sugar

x kg of tea is equivalent to 70 kg of sugar


4 kg _________________ 8 kg


x kg _________________ 70 kg


Cross multiplication is appropriate again

X × 8 = 4 × 70

8X = 280

X = 280 / 8

x = 35 kg


35 kg of tea is equivalent to 70 kg of sugar

70 kg of sugar is equivalent to 168 kg of flour

168 kg of flour is equivalent to 24 kg of coffee


Therefore, 35 kg of tea is equivalent to 24 kg of coffee