Question

6 nuts and 5 bolts weigh 278 grams while 8 nuts and 3 bolts weigh 268 grams. Find the weigh of each nut and that of each bolt. How much do 3 nuts and 3 bolts weigh together?

Answer 1

Let the weight of each nut be x

And the weight of each bolt be y

$6x+5y=278..........(1)\\and\\8x+3y=268..........(2)\\Therefore,\\x=\frac{278-5y}{6}$

Put the value of x in the (2) equation,

$8[\frac{278-5y}{6} ]+3y=268\\\\\frac{1112-20y}{3} +3y=268\\\\\frac{1112-20y}{3} +\frac{9y}{3} =268\\\\\frac{1112-11y}{3} =268\\1112 -11y = 268 *3\\-11y = 804-1112\\-11y = -308\\11y = 308\\\\\y = 2$

Put the value of y in (1) equation

$6x+5(28)=278\\6x+140=278\\6x=278-140\\6x=138\\x=23$

Therefore, 3 nuts and 3 bolts together are

$3x+3y\\=3(23)+3(28)\\=69+84\\=153\\Ans.$