Question

the sum of three number is 56. the difference of the largest and the smallest is 50, and the sum of the two smaller number is 13. find the numbers? the three numbers, from the largest to smallest, are _,_, and _.

Answer 1

The three numbers from the largest to the smallest are:

43, 20 and -7

Step-by-step explanation:

Let the three numbers be: x, y and z.

Since their sum is 56, we have:

`x+y+z=56`

Suppose z is the largest, and x, the smallest. As their difference is 50, we have:

`z-x=50`

Lastly, given that the sum of the two smaller numbers is 13, we have:

`x+y=13`

We want to find the values of x, y and z.

Using the last equation in the first equation, we can replace (x+y) by 13 to have:

`13+z=56`

Subtracting 13 from both sides, we have:

`\begin{gathered} z=56-13 \\ z=43 \end{gathered}`

Now, using z = 43 in the second equation, we have:

`43-x=50`

Subtracting 43 from both sides

`\begin{gathered} -x=50-43 \\ -x=7 \end{gathered}`

Divide both sides by -1

`\begin{gathered} x=(7)/(-1) \\ \\ x=-7 \end{gathered}`

Finally, using x = -7 in the third equation, we have:

`-7+y=13`

Add 7 to both sides

`\begin{gathered} y=13+7 \\ y=20 \end{gathered}`

Therefore, the three numbers from the largest to the smallest are:

43, 20 and -7