Anna:
1st month = 18 + [tex]\frac{3}{4}[/tex] = 18[tex]\frac{3}{4}[/tex] inches
2nd month = 18[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 19[tex]\frac{1}{2}[/tex]
3rd month = 19[tex]\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 20[tex]\frac{1}{4}[/tex]
4th month = 20[tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 21
5th month = 21 + [tex]\frac{3}{4}[/tex] = 21[tex]\frac{3}{4}[/tex]
Grace:
Because Anna is [tex]\frac{9}{4}[/tex] inches shorter than Grace, we can start the count from the third month:
1st month = 20[tex]\frac{1}{4}[/tex]
2nd month = 21
3rd month = 21[tex]\frac{3}{4}[/tex]
4th month = 21[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 22[tex]\frac{1}{2}[/tex]
5th month = 22[tex]\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 23
