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An
Unusual Purchase
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Strategies and Hints
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n + h + t = 100
n + 10h + 50t = 500 -
The replacement set for the variables is the set of whole numbers. Negative or fractional answers would not make sense in the problem context.
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The problem might appear impossible to solve because there are three unknowns and only two equations.
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Subtracting n + h + t = 100 from n + 10h + 50t = 500 results in 9h + 49t = 400. This can be written as
h
= 44 - 5t + 
This form of the equation helps you find those values of t which will result in h being a whole number.
Solution
t
= 1 is the only integral value of t that makes sense in h = 44 - 5t
+
So, t = 1, h = 39, and n = 60. The customer bought 1 roll of electrical tape, 39 hooks, and 60 nails.
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