Carey is 12 years older than Donovan. Five years ago the sum of their ages was 28.How old are they now?

Answer 1

Hello Students,

This algebra question involves finding two unknowns, which is Carey's age and Donovan's age. In order to solve for two unknowns, we need to set up two equations relating the two unknowns and then solve it to find one of the unknowns first and then the second unknown.

Here, let the first unknown (Carey's present age) be denoted as 'C' and likewise, Donovan's present age be 'D'.

Now, let's set up the equations based on the information given.

Since, Carey is 12 years older than Donovan:

C = D + 12 ------------- Equation 1

Also, 5 years ago, their ages totaled up to 28 years:

(C - 5) + (D - 5) = 28 ------------- Equation 2

Where, (C - 5) and (D - 5) are Carey's and Donovan's ages 5 years ago (since C and D are their present ages)

Now, in equation 2, we substitute C as (D + 12) ---- using equation 1

Therefore,

[ (D+12) - 5 ] + (D-5) = 28

Solving for D...

[ D + 7 ] + (D - 5) = 28

2D + 2 = 28

2D = 26

Therefore, D = 13

Putting D = 13 in equation 1, we get:

C = 25

Hope this helps! Good luck! :)

Answer 2

Donovan = X

Carey = X+12

X + X+12 = 28

Add like terms

2X +12 = 28

Subtract 12 from both sides

2X+12-12=28-12

2X= 16

Divide both sides by 2

X=8

Now we know that Donovan was 8 and Carey was 8+12= 20; Therefore, if they are five years older, then all we need to do is add 5 to both of there ages.

Answer 3

Carey always was, is, and always will be 12 years older than Donovan.

So, five years ago, they were 12 years apart and their ages added up to 28. What two numbers work this way? You can work this problem like a puzzle and figure out what two numbers add up to 28 and are 12 apart. Then, find out how old they would be five years later.

But this is Algebra 1! We are here to work with letters and numbers and solve for x! So we can also set up equations.

Carey is 12 years older than Donovan:

C = D + 12

Pretty simple.

Five years ago the sum of their ages was 28.

(C - 5) + (D - 5) = 28

The minus five is to show that this was five years ago.

Finally, combine the two equations using the substitution method:

( (D+12) - 5) + (D-5) = 28

With only one variable in the equation, you can find out D, Donovan's age today. The plug it back in to your equation to find Carey's age.

Good luck; have fun!