Question

Three numbers X,Y, and Z are in the ratio 2:7:8. If 12 is subtracted from Y, then three numbers form a geometric sequence (in the order X,Y-12, Z). Find X,Y,and Z I got the first answer it is (8,28,32) but there is another solution please help

Answer 1

The other 3 numbers you are looking for are:

24/11

84/11

96/11

Explanation:

We can start off by making the numbers 2x, 7x, and 8x. We put them in expressions:

(7x-12)^2=2x(8x)

Simplify

49x^2-168x+144=16x^2

Subtract 16x^2 on each side

33x^2-168x+144=0

Divide by 3

11x^2-56x+48=0

Factor

(11x-12)(x=4)=0

Answer

x=4 or x=12/11

If x is equivalent to 4 then that means that the original numbers would be:

8, 28, 32

2(4), 7(4), 8(4)

Subtracting 12 from Y, or 28 will make it 16.

8, 16, 32

This seems to be a geometric progression

Next we have 12/11

2(12/11), 7(12/11), 8(12/11)

24/11, 84/11, 96/11

Subtracting 12 from Y, or 84/11 will get us -48/11, meaning r=-2 for the GP.

Final Answer:

8 , 28 , 32

24/11 , 84/11 , 96/11