Two consecutive even numbers have a product of 288. What are the numbers?
The answer I got through trial and error was 18 and 16. Is there a way for me to form the question into an equation and work that out to find the answer, instead of just guessing numbers? Thanks.
what do you know about even numbers? They differ by 2, right?
So, if the smaller number is x, then the larger one is x+2
x(x+2) = 288
now solve that.
Or, if you consider u as the number between the two even ones, then
(u-1)(u+1) = u^2-1 = 288
u^2 = 289
u=17
so the numbers are 16 and 18.
Yes, you can solve this problem by setting up an equation and solving it algebraically. Let's call the first even number x, and since the numbers are consecutive even numbers, the second even number will be x + 2.
According to the problem, the product of these two consecutive even numbers is 288. So, we can write the equation:
x * (x + 2) = 288
To solve this equation, we need to expand the left side:
x^2 + 2x = 288
Now, let's rearrange the equation to bring all terms to one side:
x^2 + 2x - 288 = 0
This is a quadratic equation, so we can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:
(x - 16)(x + 18) = 0
Setting each factor to zero and solving for x, we get:
x - 16 = 0, x = 16
x + 18 = 0, x = -18
Since we are looking for even numbers, we can discard the negative solution. Therefore, the first even number is x = 16, and the second consecutive even number is x + 2 = 18.
So, the two even numbers that have a product of 288 are 16 and 18.
Yes, you can set up an equation to solve this problem algebraically. Let's represent the first even number as x, and the next even number as x+2 (since consecutive even numbers have a difference of 2).
We know that the product of these two numbers is 288, so we can write the equation:
x(x+2) = 288
Expanding the equation:
x^2 + 2x = 288
Rearranging the equation:
x^2 + 2x - 288 = 0
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:
(x+18)(x-16) = 0
Setting each factor equal to zero:
x + 18 = 0 or x - 16 = 0
Solving for x:
x = -18 or x = 16
Since we're looking for even numbers, we can discard the negative solution. Therefore, the first even number is 16, and the next even number is 16 + 2 = 18.
So the two consecutive even numbers with a product of 288 are 16 and 18.