On a nut-a-bolt production strip, adjectives the nuts weigh like peas in a pod and adjectives the bolts weigh matching. An demand of

50 nuts and 60 bolts weighed 10.6 kg. An order of 40 nuts and 30 bolts weigh 6.5 kg. What should an order of 60 nuts and 50 bolts weigh?
Answers:
50N + 60B = 10.6
40N + 30B = 6.5 or 80N + 60B = 13

80N + 60B = 13
- (50N + 60B = 10.6)
-------------------------
30N = 2.4kg
N = 80g
B = 110g
set up a system of equations. let x be the mass of nuts, and y be the weight of bolts

50x + 60y = 10.6
40x + 30y = 6.5

multiply the second equation by -2 and combine

50x + 60y = 10.6
-80x - 60y = -13

-30x = -2.4
divde by -30 on both sides
x = 0.08 kg

plug this into one of the original equations and solve for y
50(.08) + 60y = 10.6
4 + 60y = 10.6
60y = 6.6
divide by 60 on both sides

y = .11 kg

so, 60x + 50y = ??
60(.08) + 50(.11) =
4.8 + 5.5 = 10.3 kg

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