Question

Michael is 17 years older than John. The sum of their ages is 49. Find Michael's present age.

Answer 1

Michael is 33 yrs old. John is 16 yrs old.

Explanation:

Let M = Michael's age

Let J = John's age

M + J = 49

M-17 = J

Substitute the 2nd equation for J in the 1st equation and solve for M.

M + J = 49

M + (M-17) = 49

2M - 17 = 49

2M = 49+17

2M = 66

M = 33

So Michael is 33.

M + J = 49

33 + J = 49

J = 49-33

J = 16 John is 16.

Check that the answers work

33-16 = 17

33+16+49

Answer 2

John is 16 and Michael is 33

Explanation:

(Let John’s age be x)

Michael is 17 years older than John.

• m = x + 17

The sum of their ages is 49. So:

• x + (x + 17) = 49

Simplifying the equation:

• 2x + 17 = 49

Subtracting 17 from both sides gives:

• 2x = 32

Dividing both sides by 2 gives:

• x = 16

So, John is 16 years old. If Michael is 17 years older, we can add 17 to 16:

• 17 + 16 = 33

Therefore, John’s age is 16 and Michael’s age is 33.