Arithmetic Mean!

Algebra Level 4

Four positive integers are given.Select any three of these integers and find their A.M.,and add to this result add the fourth number.If the four answers thus got are $17,21,23,29$ , then find the original numbers.

Input your answers as the sum of these four numbers.

The answer is 45.

1 solution

Khang Nguyen Thanh
Aug 11, 2015

Let $a,b,c,d$ are 4 given numbers.

So, the four answer thus got are $\dfrac{a+b+c}{2}+d$ , $\dfrac{b+c+d}{2}+a$ , $\dfrac{c+d+a}{2}+b$ , and $\dfrac{d+a+b}{2}+c$ .

Adding 4 above numbers, we get: $2a+2b+2c+2d=17+21+23+29=90$

Hence, $a+b+c+d=\boxed{45}$ .

Can u find the value of a,b,c,d?Actually I wanted to ask this as the question but I thought of changing it slightly!!

naitik sanghavi - 5 years, 10 months ago

3a + b + c + d = 51
3b + a + c + d = 63
3c + a + b + d = 69
3d + a + b + c = 87

2a + 45 = 51 --> a = 3
2b + 45 = 63 --> b = 9
2c + 45 = 69 --> c = 12
2d + 45 = 87 --> d = 21

Vincent Miller Moral - 5 years, 10 months ago

You made it easy by asking the sum. We only had to add all the numbers and then divide by 2. If you want people to find all the numbers then you could probably ask the product of the 4 numbers

Kushagra Sahni - 5 years, 10 months ago

Yes,you are right!!

naitik sanghavi - 5 years, 10 months ago

@Naitik Sanghavi – You can edit it and after that it can be a better problem and we will have to do more work.

Kushagra Sahni - 5 years, 10 months ago

Arithmetic Mean!

The answer is 45.

1 solution

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