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Can someone please help me with this word problem? |
Mr. Schwinn was taking inventory at his shop. He sells bicycles and tricycles. He counted 127 wheels and 106 pedals. How many bicycles and tricycles does he have in his store? Hello Jolie, Let us say that there are t tricycles and b bicycles. Then for every trike there are three wheels so we have 3t wheels and for every bike we have two wheels so we have 2b wheels. Therefore: 3t +2b = 127 Also, for every trike we have two pedals so we have 2t pedals and for every bike we have 2 pedals hence 2b pedals. Ergo 2t + 2b = 106 Now subtract the second equation from the first and we get: t = 21 So we have 21 trikes. Putting this back into the second equation gives us: 2(21) + 2b = 106 or 42 +2b = 106 hence 2b = 106 - 42 so 2b = 64 and b = 32.. So we have 32 bikes and 21 trikes. Checking: 2(21) + 2(32) = 42+64=106 3(21) + 2(32) = 63 + 64 = 127 Hope this helps. Total number = pedals / 2 = 53 127 = 3T + 2B T+B=53 You should be able to solve that ok, you know that he has 106 pedals, and regardless of what kind of bike it is, it has two pedals, so divide it by two Now you know that he has 53 bikes think of a bike as x then a tricycle is (x + 1) so x + (x+1) = 53 subtract the 1 and 2x = 52 x = 26 so he has 26 bikes subtract 26 from 53 and you get the number of tricycles 27 tricycles Hope that helped! There are 3 steps here: Let letters be the unknowns, change the word statements into equations, and solve them. Let there be B bicycles and T tricycles. Then the statement about wheels translates to: 2B + 3T = 127 and the one about pedals... 2B + 2T = 106. Easiest way to solve these 2 equations in 2 unknowns is to substract the lower from the upper. This leaves T = 127-106 = 21. To get B, put the answer for T back in one of the original equations. Use the second: 2B + 2(21) = 106, or 2B + 42 = 106 Then 2B = 106-42 = 64, and B = 32. If you only need to know how many TOTAL of the bikes and trikes he has, then divide 106 by 2. Both kinds have only two pedals each. That means that 127 wheels is just there to confuse you. If you need to know how many of EACH, then subtract 106 from 127. That gives you the number of trikes. From above, you know how many total units you have, so subtract the number of trikes from that number to tell you how many bikes you have. To check yourself, multiply 3 and the number of trikes, and 2 times the number of bikes. The sum will confirm the number of wheels. T=# of trikes B=# of bikes 3T + 2B = 127 // times by 3 and 2 for # of wheels T + B = 53 T = 53 - B Substituting: 3(53-B) + 2B = 127 159 - 3B + 2B = 127 159 - B = 127 -B = -32 B = 32 T + B =53 T + 32 = 53 T = 53-32 T = 21 There are 21 Trikes and 32 Bikes Guess & Check 21 Tricycles 32 Bicycles |
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