Math question?

Question

Here is a 5th grade math problem . Please help.

The product of two numbers is 128 and their quotient is 8. What are the numbers?

Answer 1

xy = 128
x/y = 8

x = 8y

8y² = 128
y² = 128/8
y² = 16

So y is either -4 or 4.

The answers are:

32 and 4
or
-32 and -4

Answer 2

Let x be one number and y be the other. Then we know x*y = 128 and x/y = 8. Solve for x in the second equation:

x = 8y. Then substitute this into the first equation:
(8y) * y = 128
8y^2 = 128, divide by 8 to get
y^2 = 16. Therefore y = 4 or -4. Substitute these back into one of the original two equations to get x.

If y = 4, since xy = 128, 4x = 128 so x = 32.
If y = -4, since xy = 128, -4x = 128, so x = -32.

So the two numbers are either 4 and 32, or -4 and -32.

Answer 3

product is what you get when you multiply.
quotient is when you divide.

You can give variables to the numbers to figure them out.
Make the first x and the second y, so

x * y = 128

x / y = 8.

Now you can either multiply or divide to find one variable with respect to the other. Multiply both sides of the second equation by y.

(x / y) * y = 8 * y

The y's on the left side cancel out--y / y = 1, so you have

x = 8y.

You then take the other equation,

x * y = 128

and you can replace x by 8y so you have only y's in the second equation.

x * y = (8y) * y = 128.

8y * y = 128.

Divide both sides by 8.

y * y = 16.

y * y = y^2 (y-squared).

So you need to know the square root of 16 to find out what y is. What times itself is equal to 16? If you're not sure, you can plug it into your calculator.

4 * 4 = 16.

so you have y = 4.

Then take either one of the equations to find x.

x * y = 128.

x * 4 = 128

Divide both sides by 4.

128 / 4 = 32 = x

So you know x and y. Those are your numbers!

4 and 32!

Answer 4

4 and 32

Answer 5

x=32
y=4