Question

3 numbers add up to 100
The difference between the 2 largest numbers is 12.
The difference between the 2 smallest is 2.
What are the numbers?

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Answer 1

Answer:

Let the 3 numbers be X,Y and Z. Arbitrarily let Z be the largest, Y be the next largest and X be the smallest.The equations are:

X + Y + Z = 100.

Z - Y = 12

Y - X = 2

So it follows that:

4, X = Y - 2

Substituting in equation 1 the value for X using equation 4 we obtain:

5. Y - 2 + Y + Z = 100.

Simplifying we get:

6. 2Y + Z = 102

And we have from equation 2 (by rewriting it):

7. -Y + Z = 12

Now multiply equation 7 by 2 to obtain:

8. -2Y +2Z = 24

Adding equations 6 and 8 we obtain:

9. 3Z = 126

So we have by dividing 126 by 3.

10. Z = 42

Replacing Z in equation 2 with its value we obtain:

11. 42 - Y = 12

So we now have:

12. Y = 30.

Replacing Y in equation 3 we obtain:

13. 30 - X = 2

So we get:

14. X= 28.

Checking our work:

From equation 1:

15. 28 + 30 + 42 = 100 (check!)

From equation 2:

16. 42 – 30 = 12 (check!)

From equation 3:

17. 30 - 28 = 2 ( check!)

Answer 2

Answer:

hi

Step-by-step explanation:

the answer is in the attachment