# Answer to Question #29217 in Differential Equations for wizzie

Question #29217

The mean age of 4 women is 19 years 11 month. When a fifth woman joins them, the mean age of all 5 is 20 year 7 month. How old is the fifth woman?

Expert's answer

Let's denote the ages of five women by a1, a2, a3, a4 and a5 respectfully. Then we have a system of equations:

(a1+a2+a3+a4)/4 = (19*12 + 11) = 239 (1)

(a1+a2+a3+a4+a5)/5 = (20*12 + 7) = 247 (2)

Let's solve it for a5.

(1) ==> a1+a2+a3+a4 = 4*239 = 956 (3)

(2) ==> a1+a2+a3+a4+a5 = 5 * 247 = 1235 (4)

Substituting for (3) into (4) we get:

956 + a5 = 1235 ==> a5 = 279

So, the age of the fifth woman is 279 month, or 23 years 3 month.

(a1+a2+a3+a4)/4 = (19*12 + 11) = 239 (1)

(a1+a2+a3+a4+a5)/5 = (20*12 + 7) = 247 (2)

Let's solve it for a5.

(1) ==> a1+a2+a3+a4 = 4*239 = 956 (3)

(2) ==> a1+a2+a3+a4+a5 = 5 * 247 = 1235 (4)

Substituting for (3) into (4) we get:

956 + a5 = 1235 ==> a5 = 279

So, the age of the fifth woman is 279 month, or 23 years 3 month.

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