## Liz planted a tree.?

Heres my approach: An increase by 125% means the new height is 2.25 times greater than the original height (i.e. the original height plus the increase). For an original height of A feet and B inches, this is the same as an original height of 12A+B inches. This is so that we can do all the initial calculation work in inches. Similarly the new height of B feet and A inches is 12B+A inches. Therefore we can state that 2.25 times original height = new height, or 2.25(12A+B) = (12B+A) 27A+2.25B = 12B+A so that 26A = 9.75B or B = 2.666A Since B < 12 and A and B are positive integers (from the question), this limits the range of values that A and B can take. For example, the maximum value of B is 11 inches however this gives an non-integer value of A (i.e. 4.125). The maximum integer value of A is therefore 4, but this would mean a non-integer value of B (i.e. 10.666 inches). Looking more carefully at the value of 2.666 we could guess that A might be 3, 6, or 9 to get an integer value of B but only one of those satisfies the condition B < 12. So setting A=3 gives B=8, i.e. an original height of 3 feet 8 inches (or 44 inches). This would mean a new height of 8 feet and 3 inches (or 99 inches), which is indeed 2.25 times greater. Therefore A+B=3+8=11