Comparing Numbers: Two Equations, Two UnknownsDate: 01/14/98 at 17:38:46 From: Charles Tollefson Subject: A problem I'm having trouble with. Here's the Problem: One number is 25% of another. The larger number is 12 more than the smaller. What are the numbers? What formula can I use to find the answer? Date: 01/14/98 at 18:58:14 From: Doctor Barney Subject: Re: A problem I'm having trouble with. This is a classic case of two equations and two unknowns. First let's talk about the unknowns. There are two numbers, but we don't know what they are, so in order two be able to talk about them, and write equations for them, we need to make up something to call them. You can use any names you want, but in algebra it is customary to use letters, like x and y or a and b or p and q. How about we use A and B? Now we want to write equations using these letters. Read the problem carefully. The first sentence can be written as a mathematical equation: A = (25/100) x B From the second sentence, we can write another equation, keeping in mind that from the way we wrote the first equation we know that B is larger than A. B = A + 12 Now for the tricky part: if the stuff on the right side of the second equation is equal to B, we can substitute that stuff in to the first equation wherever we see a B. Then the first equation will look like: A = (25/100) (A+12) Can you simplify this expression and solve for A? After you do, take that value for A and "plug it in" to either of the original two equations to find the answer for B. The final answer is given below. (Don't look until you try it yourself.) -Doctor Barney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ ANSWER: 4 and 16 Date: 01/14/98 at 18:47:06 From: Doctor Anthony Subject: Re: A problem I'm having trouble with. Let the larger number be x. Then smaller number is 0.25x So x - .25x = 12 .75x = 12 x = 12/.75 = 16 So the two numbers are 16 and 4. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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