My Math Forum word problem. just not sure how to write words as a formula

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 11th, 2016, 02:28 PM #1 Senior Member   Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10 word problem. just not sure how to write words as a formula One number is three less than four times another. If their sum is increased by six, the result is twenty-eight. Find the numbers. The smaller of the numbers is and the larger is . So is that x-3+4(y+6)=28 ? Thanks Last edited by skipjack; February 13th, 2016 at 08:28 PM.
February 11th, 2016, 02:42 PM   #2
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x = one number

y = another number

Quote:
 One number is three less than four times another.
x = 4y-3

Quote:
 If their sum is increased by six, the result is twenty-eight.
x+y+6 = 28

solve the system of two equations

February 11th, 2016, 03:27 PM   #3
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Quote:
 Originally Posted by GIjoefan1976 One number is three less than four times another. If their sum is increased by six, the result is twenty-eight. Find the numbers. The smaller of the numbers is and the larger is . So is that x-3+4(y+6)=28 ? Thanks
We can solve this in one variable, which also helps understand the question better.

Let the smaller number be $x$.

The bigger number is $4x-3$.

According to the question,

$6+ {\large[} x + (4x-3) {\large]} = 28$

Solving for $x$, we get $x=5$

So, the smaller number is 5.

The bigger number is $4x-3=17$.

Hence the numbers are 5 and 17.

Last edited by skipjack; February 13th, 2016 at 08:27 PM.

 February 13th, 2016, 10:14 AM #4 Senior Member   Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10 Thanks to you both, it still confuses me, I will just have to remember once solving for x I need to then redo the equation once I have figured out what x was Prakhar very impressed by your being able to do it with your one variable formula!
February 13th, 2016, 07:59 PM   #5
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Quote:
 Originally Posted by GIjoefan1976 I will just have to remember once solving for x I need to then redo the equation once I have figured out what x was
You mean this:
"After solving for x, I need to substitute its value in the equation
in order to get the value of the other number."

Right?

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