Question

the average of the four successive odd number is 34.what would be the value of the smallest of these number?​

Answer 1

Answer:

31

Step-by-step explanation:

1) (x + x + 2 + x + 4 + x + 6)/4 = 34

2) x + x + 2 + x + 4 + x + 6 = 136

3) 4x + 12  =136

4) 4x = 124

5) x = 31

Answer 2

1

1

The average of four consecutive odd numbers is 24. What is the smallest number?

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Bill Palmer

Answered 1 मई 2018

The average of two numbers is their midpoint on a number line. If you wanted two consecutive odd numbers whose average was 24, obviously your choice would be 23 and 25, because 23 is the largest odd number less than 24, and 25 is the smallest odd number greater than 24. Great, so we have 2 consecutive odd numbers that have an average of 24. Too bad we need 4 of them, right? Not a problem - we just need to take the next odd number in each direction and add them to our pair. Instead of 23 and 25, now we have 21 and 23 and 25 and 27. Average is still 24. The smallest of those 4 is 21.

If you wanted to do this with algebra, let x be the smallest number. Then the next 3 numbers are x+2, x+4 and x+6. To take the average, add them up and divide by the number of numbers:

$\frac{(x + x + 2 + x + 4 + x + 6)}{4}$

We want that average to equal 24, so we set it equal to 24 and solve for the value of x, which is the smallest of the 4.

(x + x + 2 + x + 4 + x + 6)/4 = 24

multiply both sides by 4 and collect like terms:

4x + 12 = 96

solve for x:

4x = 84

x = 21

Notice that we don’t have to do anything special to force our value of x to be odd - there is only 1 solution to the constraints imposed by the problem, so either our answer will be odd, or there is no answer (or we made a mistake working it). Try solving a different version of this problem: find the smallest 5 consecutive even integers whose average is 24. You can set up the algebra the same way.