# The product of three integers is 90. The second number is twice the first number. The third number two more than the first number. What are the three numbers?

Oct 25, 2017

$22 , 44 , 24$

#### Explanation:

We assume the first number to be x.
First number = $x$

"twice the first number"
Second number = $2 \cdot \text{first number}$
Second number = $2 \cdot x$

"two more than the first number"
Second number = $\text{first number} + 2$
Third number = $x + 2$

The product of three integers is 90.
$\text{first number" + "second number" + "third number} = 90$
$\left(x\right) + \left(2 x\right) + \left(x + 2\right) = 90$

Now we solve for x
$4 x + 2 = 90$
$4 x = 88$
$x = 22$

Now that we know what x is, we can plug it in to find each individual number when $x = 22$
First = $x = 22$
Second = $2 x = 2 \cdot 22 = 44$
Third = $x + 2 = = 22 + 2 = 24$
The passage contains a mathematical word problem asking for three integers that meet specific conditions, and it provides a solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# The product of three integers is 90. The second number is twice the first number. The third number two more than the first number. What are the three numbers?

Oct 25, 2017

$22 , 44 , 24$

#### Explanation:

We assume the first number to be x.
First number = $x$

"twice the first number"
Second number = $2 \cdot \text{first number}$
Second number = $2 \cdot x$

"two more than the first number"
Second number = $\text{first number} + 2$
Third number = $x + 2$

The product of three integers is 90.
$\text{first number" + "second number" + "third number} = 90$
$\left(x\right) + \left(2 x\right) + \left(x + 2\right) = 90$

Now we solve for x
$4 x + 2 = 90$
$4 x = 88$
$x = 22$

Now that we know what x is, we can plug it in to find each individual number when $x = 22$
First = $x = 22$
Second = $2 x = 2 \cdot 22 = 44$
Third = $x + 2 = = 22 + 2 = 24$
user
The passage contains a mathematical word problem asking for three integers that meet specific conditions, and it provides a solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER