Answers:
There are two possible outcomes
- The integers are 0 and 2
- The integers are 34 and 36
If your teacher wants only positive integers, then go for the second scenario.
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Step-by-step explanation:
x = smaller integer
x+2 = larger integer
We can see that x+2 follows directly after x, so they are consecutive. Also, there's a gap of 2 units between the values. This is due to the phrasing "consecutive even" instead of just "consecutive".
Their product is x(x+2) = x^2+2x
Their sum is x+(x+2) = 2x+2
The product is 36 less than 18 times their sum, which means,
product = 18*(sum) - 36
x^2+2x = 18(2x+2) - 36
x^2+2x = 36x+36-36
x^2+2x = 36x
x^2+2x-36x = 0
x^2-34x = 0
x(x-34) = 0
x = 0 or x-34 = 0
x = 0 or x = 34
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If x = 0, then x+2 = 0+2 = 2
The product is x*(x+2) = 0*2 = 0
The sum is x+(x+2) = 0+2 = 2
If we multiply the sum by 18, then we get 18*2 = 36. Subtracting off 36 leads to 36-36 = 0
Therefore the equation below
product = 18*(sum) - 36
has been satisfied
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If x = 34, then x+2 = 34+2 = 36
product = x*(x+2) = 34*36 = 1224
sum = x+(x+2) = 34+36 = 70
then we can see that...
product = 18*(sum) - 36
1224 = 18*(70) - 36
1224 = 1260 - 36
1224 = 1224
So that works as well.
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There are two possible outcomes
Either the integers are 0 and 2
OR
the integers are 34 and 36