Answer to Question #13078 in Math for kate7

Question

Paul's three children have birthdays in the same week. He bought a circular birthday cake and divided the cake in proportions to their ages (105degrees, 135degrees and 120degrees). If none of his children is older than 17, what is the sum of their three ages?
a)24
b)28
c)32
d)36
e)40

Answer 1

Let's denote Paul's children ages by m, n and k. Then we have the following system:

m<17
n<17
k<17
m:n:k = 105:135:120
m, n, k є N

m/n = 105/135 = 21/27
m/k = 105/120 = 21/24
n/k = 135/120 = 27/24

m = 21/24 k
n = 27/24 k

Let k = 8. Then m = 7 and n = 9, so m+n+k = 7+8+9 = 24 (a).