Its a special day in the Brown family Its Nana Browns 84th b

It’s a special day in the Brown family. It’s Nana Brown’s 84^th birthday. Furthermore, Nana remarks that her age is now equal to the sum of the ages of her eight grandchildren.

Ben is twice the age of Anna and Chloe is three years older than Ben. Doug is half Anna’s age and Emma is five times as old as Doug. Fiona is thirteen years older than Doug. Glen’s age is eight more than the sum of Ben and Doug’s ages. Hannah’s age is the square of Anna’s age.

Find Anna’s age.

a. 2

b. 3

c. 4

d. 5

Solution

nana =84 years= sum of age of eight grandchildren

ben =2*anna
chloe =ben +3
doug= anna/2
emma = 5*doug
fiona=doug+13
glen= ben+doug+8
hannah= anna*anna

so, 84=anna+ben+chloe+doug+emma+fiona+glen+hannah
84= anna+ 2anna+ 2anna+3 + anna/2 + 5anna/2 + anna/2 +13 + 2anna+anna/2 +8 + anna*anna

60 = 11anna +anna^2

so, anna=4