Question 120448: Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The first sentence of the problem indicates that you are looking for two numbers. It also tells
you that there is a larger number (let's call it L) and as smaller number (let's call it S).
Finally, it tells you that 3 times the larger (3*L) is equal to 4 times the smaller (4*S).
In equation form this can be written as:
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3*L = 4*S
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The sum of the numbers is 21. Therefore, another equation is:
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L + S = 21
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Let's solve these two equations by substitution. We can start by solving the second equation
for L by subtracting S from both sides to leave just L by itself on the left side. When
you subtract S from both sides, the equation becomes:
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L = 21 - S
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Now let's substitute the right side of this equation for L in the first equation that we wrote.
The first equation is:
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3*L = 4*S
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substituting 21 - S for L changes the equation to:
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3*(21 - S) = 4*S
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Do the distributed multiplication on the left side by multiplying 3 times each of the terms
in the parentheses. 3 times 21 is 63 and 3 times -S is - 3*S. This changes the left side and
the equation becomes:
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63 - 3*S = 4*S
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Get rid of the -3*S on the left side by adding +3*S to both sides. On the left side, this
addition cancels the -3*S and on the right side the 3*S and 4*S add to give 7*S. So the
changed equation is:
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63 = 7*S
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Solve for S by dividing both sides of the equation by 7. This makes the answer for S:
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S = 63/7 = 9
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Now you know that the smaller number is 9. And since the total of the two numbers is
21, the larger number is 21 - 9 = 12.
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Check: 3 times the larger number is 3*12 = 36. And 4 times the smaller number is 4*9 = 36.
This means that 3*L = 4*S
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And L + S is 12 + 9 and that does equal 21, just as it should.
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Therefore, the answers of 12 and 9 satisfy the problem and are, therefore, the correct answers.
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Hope this helps you to understand the problem.
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