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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?

User YKY
by
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2 Answers

10 votes

Answer:

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.

User Mzgajner
by
9.0k points
4 votes

Answer:

  • 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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User Fanta
by
7.9k points

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