Could someone please help me?

Question

could someone help with this?
One number is 2 more than 2 times another. Their product is
40 Find the numbers.

Their numbers are _______ and _______ or ________ and _______

0 1

could someone help with this?

One number is 2 more than 2 times another. Their product is 
40 Find the numbers.

 

Their numbers are _______ and _______ or ________ and _______ 

Answer 1

This is a system of equations.

The first one states that one number is 2 more than 2 times the second number. Let's assign a as the first number, and b as the second:

 

a = 2b + 2

 

The second equation states that the product of these two number is 40:

 

a x b = 40

 

Now, in the first equation, a is defined using b. This means that we can substitute the right side of the first equation for a in the second equation:

 

(2b + 2) x b = 40

 

Now we have one variable to solve for (right now anyway).

 

2b² + 2b = 40           Divide by 2 on both sides

b² + b = 20               Subtract 20 from both sides

b² + b - 20 = 0         Use the quadratic equation or completing the square to simplify

(b + 5)(b - 4) = 0      Set both sets of parentheses equal to 0

b + 5 = 0, b = -5

b - 4 = 0, b = 4

 

Notice that we have 2 answers for b. We can take these answers and plug them back in to the first equation to solve for a:

 

a = 2b + 2

a = 2(-5) + 2

a = -10 + 2

a = -8

 

a = 2b + 2

a = 2(4) + 2

a = 8 + 2

a = 10

 

So our 2 answers are -5 and -8, or 4 and 10. We should check to make sure that they work, however, by plugging them into the second equation:

 

a x b = 40

-5 x -8 = 40         This is correct, so -5 and -8 is an answer

 

a x b = 40

4 x 10 = 40          This is also correct, so 4 and 10 is also an answer.