The Camp (Introducing new variables)

Algebra Level 2

Sometimes, a problem can be solved easily by introducing some simple new variables to it. Try this technique on the problem below that doesn't require equations.

In a camp there are 90 children and their supplies last for 20 days. After 4 days, 10 of the children left the camp. For how many days do the supplies left last for the remaining children?

16 20 17 18

2 solutions

Chris Toubezoglou
Mar 13, 2019

We decide to solve this by adding a new variable : helpings . Since the food lasts for 20 days for 90 children , there are 90 * 20 = 1800 helpings . After 4 days 4 * 90 = 360 helpings were consumed , so 1440 helpings remain . As 10 children left , the remaining food lasts for 1440 / 80 = 18 days . You can solve this problem with many ways , but introducing a new variable makes the problem very easy to solve .

After 4 days, theres food left for 16days for 90ppl. 80 is 8/9 so the duration increases by 9/8. 9/8 * 16 =18

Even simpler, still useful concept!

Eric Scholz - 2 years, 3 months ago

Well , this another simple way to do it , but I wanted to give a problem-solving technique that isn't so well known . (Fun fact : I originally intended to give the solution you gave !)

Chris Toubezoglou - 2 years, 3 months ago

@Chris Toubezoglou , we don't need any space before punctuation marks such as comma (,), full-stop (.) and question mark (?). I have done the changes for you.

Chew-Seong Cheong - 2 years, 2 months ago

Chew-Seong Cheong
Mar 14, 2019

Measure the supplies by $\text{child-days}$ . At the beginning the supplies is $\text{90 children} \times \text{20 days} = 1800 \text{ child-days}$ . After 4 days, the remaining supplies is $1800 - 90 \times 4 = 1440 \text{ child-days}$ . Since there are 80 children left after 4 days, the remaining supplies will last $\dfrac {\text{1440 child-days}}{\text{80 children}} = \boxed{18} \text{ days}$ .

The Camp (Introducing new variables)

2 solutions

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