SOLUTION: Find 4 consecutive even integers where the product of the two smaller numbers is 56 less than the product of the two larger numbers.

Question 202378: Find 4 consecutive even integers where the product of the two smaller numbers is 56 less than the product of the two larger numbers.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
smallest number is x
next larger number is x + 2
then x + 4
then x + 6
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they go up by 2 because they are even integers.
if they were odd integers they would still go up by 2.
your answer, in this case, however, should be an even integer.
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problem states that product of 2 smaller numbers = product of 2 larger numbers minus 56.
x * (x+2) = (x+4)*(x+6) - 56
expanding this makes it:
=
subtract from both sides of the equation to get:
0 =
which becomes:
0 =
add 56 and subtract 24 from both sides of the equation to get:

simplify to get:

divide both sides of the equation by 8 to get:

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smallest number is 4.
next largest number is 6
then 8
then 10
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4*6 = 24
8*10 = 80 - 56 = 24
product of the smallest numbers = product of the largest numbers - 56 so your answer is good.
answer is:
the 4 consecutive even numbers are: 4,6,8,10
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