If you add natalie's age and fred's age, the result is 39. if you add fred's age to 3 times natalie's age, the result is 65. write and solve a system of equations to find how old fred and natalie are.
Accepted Solution
A:
-------------------------------------------------------- Define x and y : -------------------------------------------------------- Let Natalie's age be x. Let Fred's age be y.
-------------------------------------------------------- Construct equations: -------------------------------------------------------- Add Natalie's age and Fred's age, the result is 39 ⇒ x + y = 39
Add Fred's age to 3 times Natalie's age, the result is 65. ⇒ y + 3x = 65
-------------------------------------------------------- Solve x and y : -------------------------------------------------------- x + y = 39 -------------- (1) y + 3x = 65 ------------ (2)
-------------------------------------------------------- From Equation (1) : -------------------------------------------------------- x + y = 39 x = 39 - y
-------------------------------------------------------- Sub x = 39 - y into equation (2) : -------------------------------------------------------- y + 3x = 65 y + 3(39 - y) = 65 y + 117 - 3y = 65 2y = 52 y = 26
------------------------------------------------------- Sub y = 26 into equation 1 : ------------------------------------------------------- x = 39 - 26 x = 13
------------------------------------------------------- Find their age : ------------------------------------------------------- Natalie = x = 13 Fred = y = 26
--------------------------------------------------------------------------------------------------------- Answer : Natalie is 13 years old and Fred is 26 years old. -------------------------------------------------------------------------------------------------------