SOLUTION: Mary collected $2.75 in nickels and dimes. Ten less than twice the number of nickels represents the number of dimes she has. How many of each kind of coin did Mary collect?

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Question 918073: Mary collected $2.75 in nickels and dimes. Ten less than twice the number of nickels represents the number of dimes she has. How many of each kind of coin did Mary collect?
Answer by srinivas.g(540) About Me  (Show Source):
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A dime is worth 2 nickels.
let no of dimes be x
let no of nickles be y
so as per the data mentioned in the question , x=2*y-10
total amount = $2.75
so total amount should comprise of nickels and dimes
x*dimes + y*nickels = $2.75
x*( 2 nickels)+ y *nickels = $2.75
=> nickles( 2x+y) = $ 2.75
but 20 nickels = 1 dollar
nickles(2x+y) = 2.75*20 nickels
cancelling nickles on both sides
2x+y = 55
already we know that x= 2y-10
so 2(2y-10) +y= 55
4y-20+y=55
5y -20 =55
add 20 on both sides

5y-20+20=55+20
5y=75
divide with 5 on both sides
5y/5 =75/5
y= 15
so x= 2y-10
x= 2*15-10
x= 30-10
x= 20
so no of dimes =20
no of nickels =15