Question

The sum of three numbers is 78. The third number is 7 more than the first. The second number is 3 times the third. What are the numbers?

Answer 1

10+51+17=78

Explanation:

Alright, so at first I just took a random number and kept on working it out until I got the exact answer as 78. Finally, i got the third number as 17. Now, i know the third number is 7 more than the first so I have to subtract 17 and 7, 17-7=10. So the first number is 10. Ok, now i know that the second number is 3 times the third number (17) so you should multiply, 17x3=51. 51 is the 2nd number.

1st number=10

2nd number=51

3rd number=17

Add them, 10+51+17=78.

Answer 2

• First number = 10
• Second number = 51
• Third number = 17

Explanation:

In the question we are given ,

• Sum of three numbers is 78

• Third no. is 7 more than first

• Second no. is 3 times third

So , we are assuming that ,

• Let first no. be x

• Third no. be x + 7 ( because in question it is given that third number is 7 more than the first number ) .

• Second no. be 3 ( x + 7 ) ( because in the question it is given that second no. is three times the third )

We are finding the solution by adding all these term and equating it with 78 because sum of these three numbers is equal to 78 .

Here we go ,

`\longrightarrow \: x + 3(x + 7) + x + 7 = 78`

Step 1 : Solving the bracket part :

`\longrightarrow \: \blue{x }+ \blue{ 3x} + \red{21} + \blue{ x} + \red{7 }= 78`

Step 2 : Adding like terms :

`\longrightarrow \:5x + 28 = 78`

Step 3 : Transposing 28 to right hand side :

`\longrightarrow \:5x = \green{78} - \green{28}`

Step 4 : Subtracting 28 from 78 :

`\longrightarrow \:5x = 50`

Step 5 : Transposing 5 to right hand side :

`\longrightarrow \:x = \cancel (50)/(5)`

Step 6 ; Cancelling 50 with 5 :

`\longrightarrow \: \purple{\boxed{x = 10}}`

Therefore value of ,

• x [ first number ] = 10

• 3(x + 7 ) [ second number ] = 51

• x + 7 [ third number ] = 17

Verification :

We are verifying our answer by adding the three numbers and it must be equal to 78 .

• 10 + 51 + 17 = 78

• 61 + 17 = 78

• 78 = 78

• L.H.S = R.H.S

• Hence , Verified.

Therefore , our answer is correct .

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