Question 497559: Nicholas is a toy collector and is investing in Webkins stuffed animals. He purchased some basset hounds for $50 each and twice as many black cats for $13 each. If Nicholas spent a total of $304, how many basset hounds and how many black cats did Nicholas purchase?
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! Another great example of a problem with 2 equations and 2 unknowns. Pretty straightforward once you get the method down:
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Let b = # of Basset Hound webkins
Let c = # of black cat webkins
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Givens:
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Basset Hounds cost $50 ea
black cats cost $13 ea
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We were given two facts that can be modeled with equations:
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Twice as many black cats as Basset Hounds:
c = 2b
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The # of Basset Hounds at $50 each + # of black cats at $13 each, Nicholas spent $304
50b + 13c = 304
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We like to find a way to use these two equations so that we can solve for one unknown and then take that new value and plug into one of the equations to determine the other unknown. One easy way to do this is rewrite one of the equations so it is in the form: unknown = other unknown plus all other terms. But we already have that from our first equation (bonus!):
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So, let's take the c = 2b from the first equation and plug it into the 2nd:
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50b + 13(2b) = 304
50b + 26b = 304
76b = 304
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divide both sides by 76 to solve for b:
b = 4
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go back to c = 2b to find c:
c = 2(4)
c = 8
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ALWAYS check your work:
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50(4) + 13(8) = 304
200 + 104 = 304
304 = 304 is true.
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Nicholas buys 4 Basset Hounds and 8 black cats for $304
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Cheers,
Lee
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