The smallest whole number of inches that could be my sister's height = 55 inches
Let my siter's height be m inches and my height be n inches.
I am more than $2$ inches taller than my sister.
so, we get an equation,
n = 2 + m ..............(1)
But if we triple her height is more than 51 inches greater than double my height.
So, we get an equation,
3m = 51 + 2n ...........(2)
We need to find the value of m.
substitute above value of n in equation (2)
3m = 51 + 2(2 + m)
3m = 51 + 4 + 2m
3m - 2m = 51 + 4
m = 55 inches
Therefore, my sister's height = 55 inches
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ4