Question

A boy imagined five positive integer numbers and told his friend that the sums of four out of five numbers he imagined are 186,203,214,228 and 233. What is the middle number that boy imagined?

Answer 1

Answer:

38

Step-by-step explanation:

Let the numbers be a, b, c, d, e

We need to find the value of c

a + b + c + d = 186                    (eq. 1)

b + c + d + e = 203                   (eq. 2)

a + c + d + e = 214                    .(eq. 3)

b + a + d + e = 228                   .(eq. 4)

b + c + a + e = 233                    (eq. 5)

Adding all equations

4 ( a + b + c + d + e) = 1064

a + b + c + d + e = 266                       ----------(eq. 6)

From eq. 4

b + a + d = 228 - e

Substituting it in eq.6

228 - e + c + e = 266

228 + c = 266

c = 38