The product of two consecutive integers is two hundred forty. Find the two integers.
The square root of 240 = 15.49
first represent unknowns using variables,,
let x = first number
let x+1 = second number
note that the second number is x+1 because they are consecutive numbers.
now we set up the equation,, according to problem, their product is 240, thus:
x(x+1) = 240
x^2 + x = 240
x^2 + x - 240 = 0
to solve for x, we can either factor it (if it's factorable) or use quadratic formula. since it's factorable, let's just factor this:
(x-15)(x+16) = 0
x = 15 and x = -16
thus there are 2 pairs of answers:
(i) x = 15 and x+1 = 16 ; and
(ii) x = -16 and x+1 = -15
hope this helps~ :)
To find the two consecutive integers whose product is 240, we can set up the equation:
x*(x+1) = 240
where x represents the first integer.
Now, let's solve the equation step by step:
1. Expand the equation:
x^2 + x = 240
2. Move 240 to the other side of the equation:
x^2 + x - 240 = 0
3. Factorize the quadratic equation:
(x + 16)(x - 15) = 0
4. Set each factor equal to zero and solve for x:
x + 16 = 0 or x - 15 = 0
x = -16 or x = 15
Since we are looking for two consecutive integers, we can disregard the negative value. Therefore, the first integer is 15.
To find the second integer, we add 1 to the first integer:
15 + 1 = 16
Hence, the two consecutive integers whose product is 240 are 15 and 16.