Laura I. answered • 10/13/15
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OK, the trickiest part is figuring out how to represent consecutive even numbers through algebra. After we figure it out, it is pretty much a matter of solving for x.
Let's start with algebraically writing three consecutive even numbers. We know that consecutive numbers are sequential, but having them all be even numbers means that the numbers must "skip" so they are not as close on the number line. We'll use x for the first number and x+2 for the second number because the other number is 2 more than the value of x. The third number would then be 4 away from x so the numbers are: x, x+2, x+4.
Let's start with algebraically writing three consecutive even numbers. We know that consecutive numbers are sequential, but having them all be even numbers means that the numbers must "skip" so they are not as close on the number line. We'll use x for the first number and x+2 for the second number because the other number is 2 more than the value of x. The third number would then be 4 away from x so the numbers are: x, x+2, x+4.
Now we'll look at "3 times the sum of the first two." We know that times means multiplication, but only the sum of the first two numbers are involved. This makes the equation look like: 3•[x+(x+2)].
The other part of the problem says "48 less than the third" so whatever the sum of the numbers are, the product is larger than the sum by 48. In other words, you must subtract 48 from the third consecutive number, which makes the other part of the equation: (x+4)-48. Putting it all together as one equation: 3•[x+(x+2)]=(x+4)-48.
As an equation, we can combine like terms (numbers with the same "tag") as well as use the distributive property. For the product of the two numbers, multiply the 3 with each term AFTER combing terms in the bracket... remember PEMDAS..., so it's now: 3•(2x+2) which is 6x+6. So now the equation is as such: 6x+6=(x+4)-48 or 6x+6=x-44. Let's have x be on one side of the equation by combining like terms again, so now the equation is 5x+6= -44 or 5x= -50. Solving for x, x= -10.
The other part of the problem says "48 less than the third" so whatever the sum of the numbers are, the product is larger than the sum by 48. In other words, you must subtract 48 from the third consecutive number, which makes the other part of the equation: (x+4)-48. Putting it all together as one equation: 3•[x+(x+2)]=(x+4)-48.
As an equation, we can combine like terms (numbers with the same "tag") as well as use the distributive property. For the product of the two numbers, multiply the 3 with each term AFTER combing terms in the bracket... remember PEMDAS..., so it's now: 3•(2x+2) which is 6x+6. So now the equation is as such: 6x+6=(x+4)-48 or 6x+6=x-44. Let's have x be on one side of the equation by combining like terms again, so now the equation is 5x+6= -44 or 5x= -50. Solving for x, x= -10.
Now that x= -10, you can determine the other two consecutive numbers. Since x= -10, then x+2 must be -8 (because -10+2= -8) so x+4 is -6. Substitute the numbers back into the algebraic equation to check if it works:
3•([-10+ (-8)]= (-6) -48 which is 3•(-18)= -54 and -54= -54!
