Solving EquationsDate: 3/23/96 at 22:15:3 From: Anonymous Subject: Solving equations Dear Dr. Math, I have a problem. Can you help? 4 3 1 ----- - ------ = ------- b b+2 b(b+2) Date: 3/24/96 at 13:15:29 From: Doctor Jodi Subject: Re: Solving equations Hi there! Since each of these terms has b and/or b+2 in the denominator, first I would multiply by b* (b+2). That gives us: 4b(b+2) - 3b(b+2) = 1b (b+2) ------ ------ ------- b b+2 b(b+2) Now we can rewrite these fractions as 4(b+2) * b - 3b * b+2 = 1 * b * b+2 - --- -- --- b b+2 b b+2 Since b/b and (b+2)/(b+2) are both equal to 1 (do you see why?) we can rewrite this again: (4(b+2) * 1) - 3b*1 = 1*1*1 which also equals 4(b+2) - 3b = 1 Now we can expand 4(b+2) by multiplying both b and 2 times 4 to get 4b+8. Does that make sense? Now let's put that back into our equation above. 4b+8 - 3b = 1 So, subtracting 3b from 4b, we get b + 8 = 1 Now, let's subtract 8 from each side: b + 8 = 1 - 8 -8 __________ b = -7 Write back if you have any questions! -Doctor Jodi, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 3/25/96 at 1:30:20 From: Anonymous Subject: Solving equations Dear Dr. Math, I have another problem: During one week in a particular city 5 percent more boys than girls were born. if the total number of babies born was 410, find the number of each. Can you help? Also: A batch of articles is sold for $810. if each article cost $43.20 and the profit made was 25 percent, how many articles were there in the batch? Thanks. Date: 3/25/96 at 11:14:15 From: Doctor Ethan Subject: Re: Solving equations Hello, These problems are very similar, so I will work one for you and explain each step, and then I will let you work the other one. Let's try to make a chart, okay? Boys * Girls * Total *********************** * * 410 We want to find out how many of each were born, so choose a letter to represent one of them. Let's let y be the number of girls born. Then how many boys were born? Well, the problem says that 5 percent more were born - this means that the number of boys = y + 5%y = y + .05y = 1.05 y So now we can fill in the chart. Boys * Girls * Total *********************** 1.05y * y * 410 So 1.05y + y = 410 So 2.05 y = 410. Now we just divide both sides by 2.05 and get y = 200 . Hope that method helps you with the next one. -Doctor Ethan, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 4/24/96 at 7:23:31 From: Anonymous Subject: Solving equations Dear Dr. Math, I have been given these equations to solve using the easiest method. I have tried all different ways but it never seems to work. Please explain. 2(x2+2x) = 4 (The two next to the x in the bracket means to the power of two.) 3b2-2b+4 = 0 (The two next to the b is also to the power of two.) Thank you for your help Date: 7/16/96 at 17:52:32 From: Doctor Alain Subject: Re: Solving equations Hello! Let's look at the first equation, 2(x^2+2x) = 4 if we divide by 2 we get x^2+2x = 2 if we substract 2 we get x^2+2x-2 = 0. To find the solution to this equation we will use the quadratic formula, which you have probably learned at school. This formula says that if ax^2 + bx + c = 0 then (i) x=(-b + Sqrt(b^2-4ac))/(2a) or (ii) x=(-b - Sqrt(b^2-4ac))/(2a). In the case in question we are trying to solve a=1, b=2 and c=-2. So we have 2 solutions, (i) x = (-2 + Sqrt(2^2-4 (1) (-2)))/(2 (1)) = (-2 + Sqrt(4 + 8))/2 = -2/2 + Sqrt(12)/2 = -1 + Sqrt(12/4) = -1 + Sqrt(3) or (ii) x = (-2 - Sqrt(2^2-4 (1) (-2)))/(2 (1)) = (-2 - Sqrt(4 + 8))/2 = -2/2 - Sqrt(12)/2 = -1 - Sqrt(12/4) = -1 - Sqrt(3). The other problem is similar and uses the same quadratic formula, but be careful, the b in the formula must not be confused with the b in the problem. -Doctor Alain, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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