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3 years ago

7

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

1 answer:

Rina8888 [55]3 years ago

6 0

Answer:

Our three numbers are 8, 48, and 16.

Step-by-step explanation:

Let the first, second, and third numbers be <em>x</em>, <em>y</em>, and <em>z</em>, respectively.

The sum of them is 72. In other words:

$x + y + z = 72$

The second number <em>y</em> is three times the third number <em>z</em>. So:

$y = 3z$

And the third number <em>z</em> is eight more than the first number <em>x</em>. 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 <em>x</em>. 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 <em>z</em> is 16.

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

Our three numbers are 8, 48, and 16.

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