Thread: Linear Applications Word Problem

Problem: The difference between two numbers is 13. Twice the smaller plus three times the larger is 129.
Answer:

I have several questions breaking down this problem:
1) How do you know which one is the smaller number in the expression above? Do you just assign and compare quantities?
2) Why does it read when the text states the difference between two numbers is 13?

Thanks for helping me understand this better.

Originally Posted by allyourbass2212

Problem: The difference between two numbers is 13. Twice the smaller plus three times the larger is 129.
Answer:
2) Why does it read when the text states the difference between two numbers is 13?

Well . That is difference.

If is any number then .

Originally Posted by Plato

Well . That is difference.

If is any number then .

That part makes sense. "The difference between two numbers is 13" when you spell it out is

But what I am failing to understand is how does that get incorporated into the final expression as

in the expression

Originally Posted by allyourbass2212

But what I am failing to understand is how does that get incorporated into the final expression as
in the expression

Well again, is smaller and is the larger.
Two times the smaller plus three times the larger equals 129.

Originally Posted by Plato

Well again, is smaller and is the larger.
Two times the smaller plus three times the larger equals 129.

In other words, how the problem is phrased is how we phrase the question.
"The difference between two numbers is 13"

Next Phrase. "Twice the smaller plus three times the larger is 129."

= smaller number
PLUS
= larger number

In other words, the only reason I know to do small number + larger number, is due to the phrase above. Is this logic correct?

2x + 3(x + 13) = 129
2x + 3x + 13 = 129
5x = 90
x = 18

so, 3x - 2x = 13
49 - 36 = 13