The sum of eli's age and cecil's age is 15. In 25 years, their combined age will be a total of twice eli's age and 4 times cecil's. How old is cecil?

Step-by-step explanation:

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

77

step-by-step explanation:

10000

step-by-step explanation: divide by 2,