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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?

 Sep 19, 2021
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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

            => 29n=2175

            => n = 2175/29 = 75

 

Thus, number of nails used to construct

Wooden cupboard = 3/5 * 75

                              = 45

 Dec 8, 2021

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