age problem algebra

Question

Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. how old is ishann now?

Answer 1

Let I be Ishaan's age.

Let C be Christophers age.

We have two equations:

I = 2C

and

I - 35 = 7(C-35) Simplify the equation

I-35 = 7C - 245

Now we will substitute 2C in for the second equation.

2C-35 = 7C - 245 Substract 2C from both sides to get the C's on the same side.

-35 = 5C -245 Add 245 on both sides to get C by itself.

210 = 5C Divide by 5

42 = C

Christopher is 42 years old. So this means that today Ishaan is 84.

Now let us check this:

35 years ago, Ishaan is 49 and Christopher is 7. So 35 years ago Ishaan is 7x as old as Christopher.

Answer 2

Today:

x represents Christopher

2x represents Ishaan

35-years ago

x - 35 represents Christopher

2x - 35 represents Ishaan

Ishaan is 7 times Christopher

2x - 35 = 7(x - 35)

2x - 35 = 7x - 245

210 = 5x

42 = x

Ishaan is 84

Answer 3

Just put the sentence into equations form, like

I = 2C ----------1 {As Ishaan is 2 times as old as Christopher }

I - 35 = 7 (C - 35) {First do 35 years ago, do -35, don't forget to do for both, as it is 35 years ago for both. After going back to 35 years do I is 7 times C }

Now, solving them we get I - 35 = 7C - 245 => I - 7C = -210

2C - 7C = -210 {from equation -----1 }

By solving, we get -5C = -210

C = 42

I = 2C => I = 2 * 42 => I = 84.

So, present age of ishaan is 84.

If you want to check the answer, whether is right or not.

As per the question, just check, 35 years ago, I = 84-35 => 49 and C = 42-35 => 7

I =49 is 7 times old as C.