Alan

Like so:

The prime factors of 66 are 2.3.11, so 4a5b72 must be divisible by these factors.

 Clearly it is divisible by 2.

For it to be divisible by 3 we must have a+b as a multiple of 3.

Try the simplest:  a = 0, b = 3:   405372/66 = 6142.

Assuming the sum of a and b is unique, then a+b = 3

To decrease a number by 40% multiply it by 0.6 (60% = 100% - 40%).

To decrease a number by 20% multiply it by 0.8 (80% = 100% - 20%)

So result = 0.8*(0.6*75) = ...  you can crunch the numbers.

The number is 110, which has factors  1, 2, 5, 10, 11, 22, 55, 110

EP's result is 720 lights.

1/3 of 720 is 240 so each small tree has 240/12 = 20 lights.

The remainder is 720 - 240 = 480 lights.  3/4 of 480 = 360 lights, so each big tree has 360/10 = 36 lights.

Therefore each big tree has 36 - 20 = 16 more lights than each small tree.

No it isn't!  EP has correctly answered the question you supplied.  If you think that answer is incorrect you might well have specified the question incorrectly.

Like so:

Let x = 0.999... etc.

Then 10x = 9.999... etc.

Subtract:  10x - x = 9.999... - 0.999...

 or                 9x = 9

so                   x = 1

Using Mathcad to do the heavy lifting I get the following:

I suspect there is a more elegant way, but I can;t think of one!

Rewrite the equations as:

y = -(A/B)x + 3/B and  y = -(1/3)x - 5/3

The values multiplying the x term constitute the slope.

Parallel lines have the same slope, so  A/B = 1/3  or  B = 3A

Since the first line passes through (-7, 2) we must have  2 = -(A/B)*(-7) + 3/B  or  2 = -(A/3A)*(-7) + 3/(3A)  or  2 = 7/3 + 1/A

Rearrange this last equation to find A, then find B (from B = 3A), then you can find B-A.