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 denotes screws and n denotes nails.
Initially, there was a total of 145 screws and
nails implies s + n = 145 (1)
Total number of nails and screws used for
wooden cupboard = 4/7s + 3/5n
After constructing wooden cupboard, equal number
of screws and nails and left,
=> S - 4/7s = n - 3/5n.
=> 7S-4S/7 = 5n-3n/5
=> 7S-4S/7 = 5n-3/5
=> 3S * 5 = 2n * 7
=> 15s - 14n = 0 (2)
(1) * 15 => 15s+15n=2175 (3)
(3) -(2) => 15n-(-14n)=2175-0
=> n = 2175/29 = 75
Thus, number of nails used to construct
Wooden cupboard = 3/5 * 75