Connections: 5X 1st of 3 consec. even integers is 14 more

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Xo Exia oX
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Connections: 5X 1st of 3 consec. even integers is 14 more

This problem baffles me.
5 times the first of 3 consecutive even integers is 14 more than 3 times the second. What is the third consecutive integer?
The equation I have so far is 5x(first integer) = 3y(second integer) + 4.

Do I solve for X? Or do I solve for Y? Or something completely different?

stapel_eliz
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There's a trick to doing this sort of "number" word problem. To learn how to use it, try here.

Once you've studied the above:

i) Pick a variable for the first of the three numbers.

ii) Use the relationship between "consecutive even [or odd] integers" to create an expression, in terms of the variable in (i), for the second of the three numbers.

iii) Following the same reasoning as in (ii), create an expression for the third of the three numbers.

Plug the variable in (i) and the expression in (iii) into the form of the equation you have already developed. Then solve the result for the value of the variable, and then back-solve for the three numbers.

If you get stuck, please reply showing your steps and reasoning, starting from the variable you picked and what it stands for. Thank you!

Xo Exia oX
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Re: Connections: 5X 1st of 3 consec. even integers is 14 more

1: X

2: Stuck here. I don't understand.

stapel_eliz
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What did the lesson say was the relationship between two consecutive even (or two consecutive odd) integers?

Xo Exia oX
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Re: Connections: 5X 1st of 3 consec. even integers is 14 more

Plus 2?

stapel_eliz
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Exactly! Even numbers are two apart; odd numbers are two apart. So given a variable (you've picked "x") for "the first even number", the "next" even number would have to be "x + 2".

Now what is the expression for the third even number?

Xo Exia oX
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Re: Connections: 5X 1st of 3 consec. even integers is 14 more

So it's 5x = 3(x + 2) +14?

X = 10

stapel_eliz
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Check your answer: If x = 10, then the second number is 12 and the third is 14. Five times the first is 50. Three times the second is 36; add another 14, and you get 50.

Since the solution "checks", then "x = 10" must be correct. Good work!

Now go back and re-read the exercise, to determine what value was asked of you. (Hint: It wasn't the value of "the first" of the three numbers.)