Reduced target distance question

[GulfCoast]

I recently got a 66% size AR 550 steel USPSA-style target for range fun. I must be math-challenged today, because I am struggling to figure this out. A 66% target at 10 yards is equal to a full size USPSA target at ??? yards? TIA, I need coffee now.

[Duces Tecum]

15.15 yards, I think.


Duces

[JCN]

15.15 yards, I think.


Duces

Although if you want to be super smarty pants about it, it’s probably a 2/3 size target rather than a true 66.0% size… so there’s that…

[CCT125US]

Target size in inches, divided by distance in yards, multiplied by desired distance gives scaled target.

For example 2" target at 10 yards
2/10 = .2 × 20 yards = 4 inch

Or 2/10 = .2 × 5 yds = 1" for closer

[T Smith]

There are a couple ways I'd approach this. I'd simplify 66% to two thirds (2/3) first. Then you could set up a proportion, comparing equal ratios. So 2:3 :: 10:x or two is to three as ten is to x. An easier way might be to use the known relationship as a scale factor. The relationship between the two distances has to be either 2/3 of 10 or its reciprocal 3/2 of 10. Logic tells you the distance will be farther than 10 yards, so multiply 10 by 3/2 and you get 15 yards.

[Jeff22]

God bless you. America needs you math people.

[rus]

Target size in inches, divided by distance in yards, multiplied by desired distance gives scaled target.

For example 2" target at 10 yards
2/10 = .2 × 20 yards = 4 inch

Or 2/10 = .2 × 5 yds = 1" for closer

Thank you