SOLUTION: 1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five. 2)Find three consecutive numbers such tha

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: 1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five. 2)Find three consecutive numbers such tha      Log On


   

Question 316791: 1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five.
2)Find three consecutive numbers such that the sum of one-third of the first and one-seventh of the second is two less that one-half of the third. Help me please.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five.
Two consecutive even numbers; x, (x+2), (we can us decimals here 2/5 = .4)
.5(x+2) - .4x = 5
.5x + 1 - .4x = 5
.5x - .4x = 5 + 1
.1x = 4
x = 4%2F.1
x = 40
40,42 are the numbers
:
Check
.5(42) - .4(40) =
21 - 16 = 5
:
;
2)Find three consecutive numbers such that the sum of one-third of the first and one-seventh of the second is two less that one-half of the third
x, (x+1), (x+2)
1%2F3x + 1%2F7(x+1) = 1%2F2(x+2) - 2
Get rid of those annoying fractions, multiply by 42, results:
14x + 6(x+1) = 21(x+2) - 42(2)
:
14x + 6x + 6 = 21x + 42 - 84
:
20x + 6 = 21x - 42
:
6 + 42 = 21x - 20x
:
48 = x
:
48, 49, 50 are the three numbers
:
Check solution
1%2F3(48) + 1%2F7(49) = 1%2F2(50) - 2
16 + 7 = 25 - 2