Writing Equations With One Variable

Question

Dontes’s age is 4 less than half of Dominic’s age. Dominic’s age is 6 more than three times Oscar’s age. The sum of their ages is 104. Find the age of each person. I need help with this i know its easy but i need recap because I totally forgot how to do it.

Answer 1

You need a bit of algebra to state what we know...

The sum of their ages is 104

(1) DON + DOM + OSC = 104

Dontes’s age is 4 less than half of Dominic’s age

(2) DON = 1/2 DOM - 4

Dominic’s age is 6 more than three times Oscar’s age

(3) DOM = 3 OSC + 6

We can eliminate the DOM variable in equation (1) and equation (2) by substituting equation (3), as follows:

DON + DOM + OSC = 104 becomes

DON + (3 OSC + 6) + OSC = 104

=> DON + 4 OSC + 6 = 104

=> (4) DON + 4 OSC = 98

and DON = 1/2 DOM - 4 becomes

DON = 1/2 (3 OSC + 6) - 4

=> DON = 3/2 OSC + 3 - 4

=> (5) DON = 3/2 OSC - 1

So now we can eliminate DON too by substituting (5) in (4), as follows:

DON + 4 OSC = 98 becomes

3/2 OSC - 1 + 4 OSC = 98

=> 11/2 OSC - 1 = 98

=> 11/2 OSC = 99

=> OSC = 99 x 2 / 11 = 18

So Oscar is 18 years old.

Go back to equation (3), so now we know Dominic is 60 years old.

Now use equation (2) to find Donte's age. Donte is 26 years old.

Double check the answer: 26 + 60 + 18 = 104 which is what we want.