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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 :)