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# The greater of two consecutive integers is 15 more than twice the smaller. Find the integers.

How do you go about solving this word problem?

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### 2 Answers by Expert Tutors

Beth L. | Patient, Knowledgeable and Very Qualified Mathematics TutorPatient, Knowledgeable and Very Qualifie...
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x = integer
x+ 1 = next (consecutive) integer

The greater integer (x+1) is (=) twice the smaller (2x)

x + 1 = 2x + 15

Put x's together and terms together on opposite sides

1 + x - x = 2x + 15 - x
1 = x + 15
-14 = x
x+ 1 = -13.

Check x + 1 = 2x + 15
substitute for x+1 and X

-13 = 2(-14) + 15
-13 = -28 + 15
-13 = -13 Correct on both sides.  There are your two answers.  I substituted -14 for X and -13 for x+1.

Katherine P. | Experienced Math and Test Prep TutorExperienced Math and Test Prep Tutor
5.0 5.0 (572 lesson ratings) (572)
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This is an algebra word problem that can be solved by setting up a system of equations. Stay with me! It only sounds complicated, but we will make it easy.

We have two consecutive integers, let's call them x and y.
Let's say y comes after x, so that means y = x+1    (consecutive numbers are in sequence, like counting, each number is 1 more than the number before it)

Now let's use our other clue from the problem. The larger number is 15 more than twice the smaller.
y is the larger number, and that is 15 more than 2 times the smaller number (x)
y = 15 + 2x

Ok, now let's use substitution.
y = x+1, so we plug that into our equation.

x + 1 = 15 + 2x

Get the variable terms on the left and the constant terms on the right.
x + 1 = 15 + 2x
- 2x             -2x

-x + 1 = 15
- 1        -1

-x    =  14
*-1       *-1

x = -14

Plug our value of x back into our definition of y.
y = -14 + 1
y = -13

So we have -14 and -13. This makes sense because integers can be negative, -14 and -13 are consecutive, and if we multiply the smaller number (-14) by 2, then add 15, we get -13. Our answer checks out!