In 5 years, the ratio of their ages will be 5:1, so the difference in their ages will be 4 ratio units. Those 4 units correspond to 32 years, so each unit corresponds to 32/4 = 8 years.
Thus, in 5 years, Kate will be 8 and her father will be 40. Right now, Kate is ...
... 8 - 5 = 3 years old.
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Using equations
Let k represent Kate's current age. Then in 5 years Kate will be k+5, and we will have ...
... 5(k+5) = (k+5)+32 . . the relationship betewen their ages in 5 years
... 5k +25 = k +37 . . . . eliminate parentheses
... 4k = 12 . . . . . . . . . . . add -25-k
... k = 3 . . . . . . . . . . . . . divide by 4
Kate is 3 years old.
