Question

Find three consecutive odd integers so that the sum of twice the first , second and three times the third is 152

Answer 1

Let the 3 odd numbers be x, x+2 and x+4.
So
2x+(x+2)+3(x+4)=152
or, 6x+14=152
or, x=138/6
or, x=23
So, the numbers are 23, 25 and 27.

Answer 2

The three unknown consecutive odd numbers are 23, 25 and 27

Solution:

We have been asked to find three consecutive odd integers so that the sum of twice the first, second and three times the third is 152

Let us consider the unknown numbers as x, y and z

We have been given that the number are consecutive odd numbers.

That means:

y = x + 2

z = y + 2

we have also been given that the sum of all three numbers is 152.

This can be written as:

2x + y + 3z = 152

We can substitute the values of y and z in the above equation to find the unknown numbers.

2x + x + 2 + 3(y + 2) = 152

3x + 2 + 3(x + 2 + 2) = 152

3x + 2 + 3x + 12 = 152

6x + 14 = 152

6x = 138

x = 23

Now, since we have the value of ‘x’ we can find the values of y and z as follows:

y= x + 2 = 23 + 3 = 25

z = y + 2 = 25 + 2 = 27

Therefore, the three unknown consecutive odd numbers are 23, 25 and 27

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