Julio has $2.75 in his pocket in nickels and dimes . the number of dimes is 10 less than twice the number of nickels. find the number of each type of coin

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 # of dimes =20  

# of nickels =15

5

step-by-step explanation: