John is 10 years older than Chris. In two years,John will be twice as old as Chris .How old are they now

Answer 1

Elise, sorry you waited so long for a response. I hope this is able to help you.

Let's look at the phrase John is 10 years older than Chris. Let's just use J to represent John and C to represent Chris. If John is 10 years older than Chris, then Chris's age + 10 years would be the same as John. Let's write this as C+10 = J or J= C+10.

Now we'll look at the second phrase. In two years, John will be twice the age of Chris. This means that when J adds to more years, (J+2), this will equal 2xChris's age in two years (2(C+2)) which equals 2C+4. So J+2=2C+4 and we can subtract 2 from either side to get J=2C+2. Now we have two equations that each give us John's current age, J=C+10 and J=2C+2. Because J stays the same, we can compare the two equations. So now let's find Chris's age by looking at C+10=2C+2. Remember, whatever we do to one side, we must also do to the other side. Now, let's make that look neater by subtracting C from both sides: 10=C+2. Now let's subtract 2 from both sides, so 8=C. So now we know Chris's age is 8! Let's look back at the equation with J in it to find John's age. Let's use J=C+10 to make this easy on ourselves. If Chris is 8, then J=8+10, so John is 18 years old. Make sure to double-check your work. If Chris is 8 and John is 18, then John is 10 years older than Chris and in two years, when John is 20, he will be twice as old as Chris in two years, who will be 10. I hope that helped!