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?
+876 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 $29:$ $n = 5 \cdot 15 = \boxed{75}$
- Jimmy
