SOLUTION: There are two numbers.When four times the larger number is added to three times the smaller number,the result is 26.If three times the larger number is decreased by twice the small

Question 1117475: There are two numbers.When four times the larger number is added to three times the smaller number,the result is 26.If three times the larger number is decreased by twice the smaller number,the result is 11.Find the numbers.
Found 4 solutions by solver91311, stanbon, greenestamps, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let represent the larger number and let represent the smaller number.

Four times the larger number:

Three times the smaller number:

Four times the larger number added to three times the smaller number is equal to 26:

Similarly:

Solve the 2X2 system of equations for and . Hint: Multiply the first equation by 2 and the second by 3, then solve with the elimination method.

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
There are two numbers.When four times the larger number is added to three times the smaller number,the result is 26.If three times the larger number is decreased by twice the smaller number,the result is 11.Find the numbers.
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Equations:
4L+3S = 26
3L-2S = 11
----------------
Modify for elimination:
12L + 9S = 3*26
12L - 8S = 4*11
---------------------------
Subtract and solve for "S"::
Smaller = 34
Larger = (11+2*34)/3 = (11+68)/3 = 79/3 = 26 1/3
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Note:: The Larger turned out to be the Smaller.
You might want to check your posting.
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Cheers,
Stan H.
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Ch
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The two equations are clearly and .

The first tutor suggested using elimination by multiplying the first equation by 2 and the second by 3 and adding; that eliminates variable y, allowing you to solve for x. Then use that value of x in either equation to find the value of y.

The second tutor tried to use elimination by multiplying the first equation by 3 and the second by 4 and subtracting to eliminate x. Unfortunately he did the subtraction incorrectly, leading to the wrong answer to the problem.

The lesson here is that it is far easier to make careless mistakes when subtracting the two equation than when adding. So for most students it is advisable to use addition instead of subtraction when using the elimination method to solve a pair of equations.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

There are two numbers.When four times the larger number is added to three times the smaller number,the result is 26.If three times the larger number is decreased by twice the smaller number,the result is 11.Find the numbers.

You don't need to recheck anything as STANBON suggests.

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