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The sum of three numbers is 72 the second number is three times the third the third number is eight more than the first what are the numbers

User Intale
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1 Answer

2 votes

Answer:

Our three numbers are 8, 48, and 16.

Explanation:

Let the first, second, and third numbers be x, y, and z, respectively.

The sum of them is 72. In other words:


x + y + z = 72

The second number y is three times the third number z. So:


y = 3z

And the third number z is eight more than the first number x. So:


z = x + 8

To find the numbers, solve for the system. We can substitute the last two equations into the first:


x + (3z) + ( x + 8) = 72

Substitute again:


\displaystyle x + 3(x+8) + x+8 = 72

Solve for x. Distribute:


x+3x+24+x+8=72

Combine like term:


5x + 32 = 72

Subtract:


5x = 40

And divide:


x=8

Thus, the first number is eight.

And since the third number is eight more than the first, the third number z is 16.

The second number is three times the third. Thus, the second number y is 3(16) or 48.

Our three numbers are 8, 48, and 16.

User Aareeph
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