Joe has a collection of nickels and dimes that is worth $7.65. If the number of dimes was doubled and the number of nickels was increased by 35, the value of the coins would be $14.30. How many nickels and dimes does he have? (Points : 20)

Question

anonymous · Answer

let number of dimes = x
and number of nickles  = y

1 dime = 10 cents
1 nickle = 5 cents

value of dimes =  10*x cents = 10x cents
value of nickles  = 5*y cents = 5y cents
they totaled to $7.65 = 765 cents

so  10x+5y=765  ----eqn(I)

number of dimes was doubled. 
so number of dimes = 2x
number of nickles was increased by 35
so number of nickles = y+35

value of dimes =  10*2x cents = 20x cents
value of nickles  = 5*(y+35) cents = (5y + 175) cents
they totaled to $14.30=1430 cents

so 20x + 5y +175 = 1430
so 20x + 5y = 1255   ----eqn(II)

solve eqn(I) and (II) to get values of x=49 and y=55

so number of dimes = x = 49
and number of nickles  = y =55