five different whole numbers are arranged in an order from the smallest to the greatest the average ofthe first - Maths - Whole Numbers

Question

five different whole numbers are arranged in an order from the
smallest to the greatest the average ofthe first three numbers is
10 the average ofthe middle three is 14 the average ofthe last
three numbers is 35 if the middle is 17,find the other four?

Pooja · Accepted Answer

Let the whole numbers be a, b, c, d, e such that a < b < c < d < e and c = 17.

We are given:

$\frac{a + b + c}{3} = 10 \Rightarrow a + b + c = 30 - - - - (1) \frac{b + c + d}{3} = 14 \Rightarrow b + c + d = 42 - - - - (2) \frac{c + d + e}{3} = 35 \Rightarrow c + d + e = 105 - - - - (3)$

putting c = 17 in (1), (2) and (3) we get

a + b =30 - 17 = 13 ----(4)

b + d = 42 - 17 = 25 ----(5)

d + e = 105 - 17 = 88 ----(6)

Now, we have four variables but three equations only, so we let a = k.

Therefore,

b = 13 - k

d = 25 - b = 25 - 13 + k = 12 + k

e = 88 - 12 - k = 76 - k

Now, can write all a, b , c, d ,e in terms of k and that is

k <</em> 13 - k <</em> 17 < 12 + k < 76 - k

Now, we can see that

k < 13 - k

⇒ 2k < 13

$k < \frac{13}{2}, t h a t i s k < 7 (b e c a u s e w e a r e g i v e n k i s a w h o l e n u m b e r a n d n o t a f r a c t i o n)$

So, a = k = 1, 2, 3, 4, 5 ,6 but only k = 6 satisfies that a a < b < c < d < e and c = 17.

Now, if we take a = k = 6, we get

b = 13 - k = 13 - 6 = 7,

c = 17 (given)

d = 12 + 6 = 12 + 6 = 18

e = 76 - 6 = 70

Thus, a = 6, b = 7, c = 17, d = 18, e = 70 is the answer.

five different whole numbers are arranged in an order from the smallest to the greatest. the average ofthe first three numbers is 10. the average ofthe middle three is 14. the average ofthe last three numbers is 35. if the middle is 17,find the other four?