SOLUTION: a,b,c and d are four consecutive even natural numbers.the sum of a and c is one fifth of the product of b and d.Find a,b,c and d.

Question 830939: a,b,c and d are four consecutive even natural numbers.the sum of a and c is one fifth of the product of b and d.Find a,b,c and d.
Answer by Elomeht(22) (Show Source): You can put this solution on YOUR website!
1. Based on the statement of the problem, we must have: b = a + 2; c = a + 4; d = a + 6
2. Based on the statement of the problem, a + a + 4 = (a + 2)(a + 6)/5
3. That is, 2a + 4 = (a^2 + 2a + 6a + 12)/5
4. Multiply the equation above by 5: 10a + 20 = a^2 + 8a + 12
5. Rearranging, we get a^2 - 2a - 8 = 0
6. Factorizing, (a - 4)(a + 2) = 0
7. The solutions to the above are: a = 4; a = -2
8. We can ignore the second solution, since a must be a natural number (that is, an integer and greater than 0)
9. So a = 4; b = 6; c = 8; d = 10
10. Let us check: a + c = 4 + 8 = 12; b times d = 6 times 10 = 60, which is 5 times (a + c)
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