Three Pieces of WireDate: 01/07/98 at 22:11:58 From: Email Subject: I need serious help Here is my math problem. I have no idea how to figure it out: A florist cuts a wire into 3 pieces. The 1st piece is 20% of the 2nd. The 3rd piece is 110% of the 2nd. The wire is 23 cm long. What is the length of each piece? Erin Date: 01/08/98 at 13:02:39 From: Doctor Joe Subject: Re: I need serious help Hi Erin, This problem requires some simple algebra: First, let x denote the length of the 2nd piece of wire (in cm). It follows that the length of the first piece, which is 20% of the first, can be expressed as (20%)*(x), where * denotes the usual multiplication. So, we have: 0.2x because 20% is actually 20/100 = 0.2 Similarly, the length of the third piece can be found: (110%)*(x) = 1.1x Finally, we add the lengths of the three pieces: First wire + Second Wire + Third Wire = Total Length So, 0.2x + x + 1.1x = 23 Then, adding the terms on the left, we have 2.3x = 23. Finally, multiplying by 1/(2.3), which is the reciprocal of 2.3, we have: x = 23/(2.3) = 10. Thus, the 2nd piece of wire measures 10 cm. The first wire is 20% of 10cm = 2cm, and the third measures 110% of 10cm = 11cm. As a last step, check that the three pieces sum to a total of 23 cm: 2 + 10 + 11 = 23. -Doctor Joe, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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