Two Numbers in 5:3 RatioDate: 12/07/2002 at 00:15:59 From: Bryan Pierce Subject: Ratios with an equation "TWO FOR TWO" Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? NOTE: There are two pairs of numbers that will make this a true statement. You need to find both of them. Your explanation must use algebra(variables and equations) to communicate the method you've used to solve the problems. I think the equation is 36+{1(x+y)} 5x 2 3y I don't know what the other equation is or how to find the numbers that make this a true statment. If you could help me I would be very appreciative. Thanks. Date: 12/08/2002 at 12:15:27 From: Doctor Mike Subject: Re: Ratios with an equation Hi Brian, This may help. Let me change notation. L means the larger and S the smaller. The first fact just says that L/S = 5/3. That's pretty simple. BUT, the NOTE you are given hints that this is a TRICK question. Why? Because "half the difference of the two numbers" can mean two different things. The difference can be either L-S or S-L. The difference L-S will be positive, and S-L will be negative. The second fact says (L-S)/2 = L-36 when you are looking for one of the solutions. The second fact says (S-L)/2 = L-36 when you are looking for the other solution. See what you can do with that. As the NOTE says, each solution will be a value for L and a value for S. Take the first equation together with ONE OF the forms of the second equation, and solve for L and S. All S and L values will be positive. Good luck. - Doctor Mike, The Math Forum http://mathforum.org/dr.math/ |
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