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

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 :)