Question

five silver coins weigh 125gm and are worth $6. Ten bronze coins weigh 500gm and are worth 80 cents. A number of silver and bronze coins which are worth $134 weigh 11kg 250gm. How many coins of each kind are their?

Answer 1

100 silver coins and 175 bronze

Explanation:

let x be the number of silver coins and y the number of bronze coins.

Worth of these coins together = 6x/(5)+0.08/(10)y

=1.2x+0.008y

Weight of one silver coin = 125/5 = 25 gm

and one bronze coin = 500/10 = 50 gms.

Weight of these coins together = 25x + 50y

Equate these two items i.e. value and weight to actuals given.

i.e. 1.2x+0.08y = 134 and ... i

25x+50y = 11 kg 250 gm = 11250 gms. ... ii

Divide the second equation by 25

x+2y = 450 ... iii

Multiply I equation by 25

30x+2y =3350 ... iv

iii-iv gives -29x = -2900 or

x =100

Substitute in x+2y = 450

2y = 350 or y =175