Question 43

Four natural numbers, when added three at a time, give the sums 180, 197 and 208 and 222. Smallest of the four numbers is

Solution

Let the four numbers be a,b,c,d. Hence a+b+c=180 a+b+d=197 a+c+d=208 and b+c+d=222

Adding all the four equations 3(a+b+c+d)= 807 or a+b+c+d= 269. To find the smallest number subtract the maximum sum i.e. 222

So b+c+d=222 and a= 269-222=47

Hence 47 is the smallest of the four numbers

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