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James used 4/7 of his screws and 3/5 of his nails to construct a wooden cupboard. In the end, he had an equal number of screws and nails left. Given that James had a total of 145 screws and nails at first, how many nails did he use to construct the wooden cupboard?

 May 14, 2021
 #1
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James used 4/7 of his screws and 3/5 of his nails to construct a wooden cupboard. In the end, he had an equal number of screws and nails left. Given that James had a total of 145 screws and nails at first, how many nails did he use to construct the wooden cupboard?

 

Let s = the number of screws

Let n = the number of nails

 

We have: $(1-\frac{4}{7})s = (1-\frac{3}{5})n$

This is equal to $\frac{3}{7}s = \frac{2}{5}n.$

We also have $n+s = 145.$

If we multiply the first equation by its common denominator namely $7 \cdot 5 = 35,$ we have that $15s = 14n.$

Multiplying the second equation by 15 we have $15n + 15s = 145 \cdot 15.$

Let’s substitute $14n$ into $15s$: $15n + 14n = 145 \cdot 15 \Rightarrow 29n = 145 \cdot 15.$

Divide both sides by $29:$ $n = 5 \cdot 15 = \boxed{75}$

 

laugh - Jimmy

 May 14, 2021
 #2
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I didn't know your name was jimmy

Guest May 14, 2021
 #3
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I don't think anyone did! cool

MathProblemSolver101  May 14, 2021

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