Writing and Solving Systems of Equations
by Chuck
The sum of Eli's age and Cecil's age is 60. Six years ago, Eli was three times as old as Cecil.Find Eli's age now.
Karin from Algebra Class Says:
In order to solve this problem, you must write a system of equations.
The first equation is pretty easy to write.
The sum of Eli and Cecil's age is 60.
Let x = Eli's age
Let y = Cecil's age
Sum means add, so:
x + y = 60
The second equation is a little tricker.
Six years ago, Eli was three times as old as Cecil.
Six years ago means we have to subtract 6
Think:
Eli (six years ago) = 3 times cecil's age (six years ago)
x - 6 = 3(y-6)
Now, let's use the distributive property.
x - 6 = 3y - 18
Next we'll get the variables on one side and the constants on the other in order to write the equation in standard form.
x - 3y - 6 = 3y -3y - 18 Subtract 3y
x - 3y - 6 = -18
x - 3y - 6 + 6 = -18 + 6 Add 6
x - 3y = -12
Now we have two equation in standard form:
x + y = 60
x - 3y = -12
You can solve easily by using substitution or linear combinations.
I will use the linear combinations method.
Step 1: Create 1 set of opposite terms.
x + y = 60
-1 ( x - 3y) = -12(-1)
x + y = 60
-x + 3y = 12
Step 2: Add
x + y = 60
-x + 3y =12
--------------
4y = 72
Step 3: Solve for y
4y/4 = 72/4
y = 18
Cecil's age is 18
Step 4: Substitute to find Eli's age.
x + y = 60
x + 18 = 60
x+18 - 18 = 60 -18
x = 42
Eli's age is 42.
Check:
42 + 18 = 60
Six years ago:
Eli was 36
Cecil was 12
Eli was 3 times as old as Cecil 6 years ago.
12 * 3 = 36
Hope this helps,
Karin