if the product of their ages is 224 how old is each child?

Question

The two Sorenson Children were born in consecutive even years.

Answer 1

suppose the younger is age N. The older must be N+2 because they were born in consecutive even years.

N(N+2) = 224
N^2 + 2n = 224
(N+1)^2 = 225
N+1 = 15
so their ages are 14 and 16

Answer 2

Let x = age of one child.

Since the age of the children are given to be consecutive, it follows that the age of the other child is (x + 1)

It is given that the product of their ages is 224, so we take the product of x and (x + 1) and equate it to 224.

x(x + 2) = 224

Now, expand the left hand side.

x^2 + 2x = 224

Move the 224 to the left hand side.

x^2 + 2x - 224 = 0

And factor.

(x + 16)(x - 14) = 0

x = {-16, 14}

This means the age of the one child is either -16 or 14. But a negative age is not possible, which means x = 14.

Given x = 14, since we know the age of the other child is
x + 2, or 16.

So the ages of the children are 14 and 16.

Answer 3

First set the age of child A to be x years old. Child B will then be (x+2) years old.

Set up an equation so that (x)(x+2)=224
If you multiply this out, you get x^2 +2x=224
subtract 224 from both sides to get the quadratic equation: x^2+2x-224=0.
If you solve this quadratic, you get that x= 14, and x=-16. Obviously, a person cannot have a negative age, so child A is 14 years old. Child B's age is 2 more than that, so child B is 16.

Answer 4

x = age of 2nd Sorenson child
x + 2 = age of 1st Sorenson child

x(x + 2)=224 ---> x^2 + 2x -224= 0

(x + 16) (x - 14) = 0 since x cannot be negative, x = 14

x + 2 = 16

The children are 16 and 14.

Answer 5

They are 14 and 16

Answer 6

14 x 16 = 224 - consecutive EVEN years.

Answer 7

Mental math: Factor 224 into two integers such that the difference of the two is 2.

224 = 14*16

Therefore, one child is 14 years old and the other is 16 years old.
----------------
Standard way:
xy = 224......(1)
x-y = 2......(2)
Combine,
x - 224/x = 2

x^2-2x-224 = 0
(x-14)(x+16) = 0

Therefore,
x = 14
y = 16

Answer 8

14 and 16

14*16 = 224

Answer 9

x(x+2) = 224

x^2 + 2x = 224

x^2 + 2x - 224 = 0

(x - 14)(x + 16) = 0

so x = 14 and - 16

negitive age doesn't make sense...so x = 14

So the ages are x and x + 2

or 14 and 16

Answer 10

one will 14 and the other 16.