Question 126447: The sum of two numbers is 89. Adding four times the first number to the second number gives 155. Express as a algebraically equation?
Found 2 solutions by praseenakos@yahoo.com, bucky:
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! Question:
The sum of two numbers is 89. Adding four times the first number to the second number gives 155. Express as a algebraically equation?
Answer:
Suppose two numbers are x and y
Sum of these number is given as 89
==> x + y = 89
Four times the first number = 4x
Adding four times the first number to the second number gives 155
==> 4x + y = 155, which is the algebraic representation of the given statementts.
You can solve these equations to get the two numbers...
Hope yopu found it useful.
Regards.
Praseena.
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! To solve this problem, you need to begin by finding two equations.
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First, let's let F represent the first number and S represent the second number.
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The first sentence of the problem tells you that if you add these two numbers, the sum is 89.
So adding them results in the equation:
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F + S = 89
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That's one equation. The you are told that adding 4 times the first (or 4F) to the second (or S)
gives 155. So you get the second equation by adding these quantities as follows:
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4F + S = 155
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You can't solve a linear equation by itself if it contains two unknowns. Therefore, you
need to figure out a way of eliminating one of the unknowns in one of the equations.
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Suppose you go to the first equation and you subtract F from both sides. This results in:
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F + S - F = 89 - F
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On the left side the F and the -F cancel each other and you are left with the equation:
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S = 89 - F
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Next, go to the second equation:
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4F + S = 155
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You now know that S = 89 - F so you can substitute 89 - F for S in the second equation to
get:
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4F + 89 - F = 155
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This new equation only has one variable ... F ... so you can solve it.
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On the left side, combine the 4F and the -F to get 3F. This reduces the equation to:
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3F + 89 = 155
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Then get rid of the 89 on the left side by subtracting 89 from both sides and you have:
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3F = 66
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Solve for F by dividing both sides by 3 and the result is:
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F = 66/3 = 22
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So now you know that F = 22. You can then return to either of the original equations,
substitute 22 for F, and solve for S. Let's go back to the first equation:
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F + S = 89
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Substitute 22 for F and this equation becomes:
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22 + S = 89
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Solve for S by subtracting 22 from both sides:
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S = 89 - 22 = 67
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So the answer is that the 2 numbers are 22 and 67.
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You can further check by substituting these numbers into the original second equation.
When you do you get:
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(4*22) + 67 = 88 + 67 = 155
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and this is what the second part of the problem tells you it should be. Therefore,
the first number of 22 and the second number of 67 check out. This answer is correct.
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Hope this helps you to work your way through the problem and understand it a little better.
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