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Find the three consecutive even integers such that five times the smallest is four times the largest

Find the three consecutive even integers such that five times the smallest is four times the largest
 
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4 Answers

Let the smallest of three be x.
The second one is x+2 (why?)
The third one is x+4; (why?)
 
It is known that 5*x=4*(x+4); Five times the smallest equals four times the largest.
 
From this, we obtain:
 
5x=4(x+4)=4x+16
x=16
 
x+2=18;
 
x+4=20:
 
Answer:
 
16,18, and 20
Beware:
x+2
x+4
are not necessarily consecutive EVEN integers; such as the case if x is ODD.  The SAT will get you on this.
 
More accurately (especially if you are a Number Theory or DIscrete Math person):
2x
2x+2
2x+4
are always consecutive EVEN integers regardless what x is.
 
5 times smallest = 4 times largest
5(2x) = 4(2x+4)
10x = 8x + 16
2x = 16
x = 8
therefore consecutive even integers are 2(8), 2(8)+2, 2(8)+4
16, 18, 20
 
 
Mental math approach:
Let a, b and c are the three consecutive even numbers. c is larger than a by 4.
Let a be equal to 4 parts, then c is larger than a by 1 parts = 2+2 = 4
So, a = 4*4 = 16.
 
Answer: 16, 18, 20
Hi Bethel -- here's a "non-formula" approach ... since 5L=4H, L must be 4/5 of H ... since H is missing 1/5, and 4 separates H from L, H needs five 4's ==> H=20 ... 16,18,20 does it :)