Question

The average of three numbers is 86. The second is 1 more than twice the first and the third is 7 less than three times the first. Find the three numbers

Answer 1

Answer:

44, 89, 125

Step-by-step explanation:

Let the first number be x, therefore,

2nd number = 1 + 2 times x = 1 + 2x

3rd number = 7 less than 3x = 3x - 7

In the given question,

Average = 86

Sum = x + (1 + 2x) + (3x - 7) = 6x - 6

Number of terms = 3

Therefore,

=> 86 = (6x - 6)/3

=> 258 = 6x - 6 => 258 + 6 = 6x

=> 264 = 6x => 264/6 = x

=> 44 = x

Required numbers are :

• x = 44

• 1 + 2x = 1 + 2(44) = 89

• 3x - 7 = 3(44) - 7 = 125

*Solved using

Average=sum/no.of quantities

Answer 2

Question

The sum of three numbers is 86 . The second number is 3 times the third. The third number is 6 less than the first. What are the numbers?

Answer

Let’s label these 3 numbers as x , y , and z .

So, we know that x+y+z=86 , y=3z , and z=x−6 . We can then replace y with 3z in the first equation to get x+3z+z=86 , x+4z=86 . Then, we can add 6 to both sides of the third equation to get x=z+6 , so we can replace x with z+6 in the first equation to get z+6+4z=86 , 5z+6=86 , 5z=80 , z=16 .

Now that we know that z=16 , we can sub in 16 for z in the second equation to get y=3(16) , y=48 .

We can also then substitute 16 for z in the third equation to get x=16+6 , x=22 .

Therefore, the three numbers are 22 , 48 , and 16