Work has to be shown my teacher said that I made some mistakes please find them and fix

Problem

Jamil always throws loose change into a pencil holder on his desk and

takes it out every two weeks. This time it is all nickels and dimes. There

are 2 times as many dimes as nickels, and the value of the dimes is $1.65

more than the value of the nickels. How many nickels and dimes does

Jamil have?

My work

*Let the number of dimes Jamil throws into the pencil holder be Y*

*Let the number of nickel Jamil throws into the pencil holder be X*

*Since there are 2 times as many dimes as nickel’s then we would have;*

*Y=2X*

*A dimes value is $0.05*

*A nickel’s value is $ 0.10*

*Since we have twice as many dimes as nickles then this would imply;*

*The sum of availables dimes and nickle is equal to $1.65*

*Converting Y=2X to a simple equation we would have;*

*Y- 2X=0 ……………………………..i*

*0.10X-0.05Y=1.65 …………….ii multiplying equation ii by 100 to get whole numbers then it will be;*

*Y- 2X=0 ………………………………i*

*10X+5Y = 165 ………………………iii*

*The least common multiple of 2 and 5 is 10. Multiply the first equation by 5 and the second equation by 2, by doing so that will have the y variable eliminated when the second equation is subtracted from the first equation.*

*(5)Y- (5)2X=(5)0 which solves to 5Y-10X=0*

*(2)10X+(2)5Y = (2)165 which solves to 20X+10Y=230*

*Subtract the second equation from the first and solve for x.*

*5Y-10X=020Y-10X=330*

*-15x**= –330divide by sides by 12 to solve for x-15 -15Y = 22*

*From the equation we can be able to conclude that jamil has 22 dimes. We can go ahead and replace the number of dimes into 1 of the equations so that we can solve for the number of nickles. Taking the second equation.*

*20X+10Y=230 since we have computed for y=2220(22)-10X=330then subtract 29.92 from both sides of the equation440 – 10X=330*

*10X= 440-330*

*10X**=110 dividing both sides by 10 we get;*

*10 10*

*X= 11 therefore jamil had 11 nickles*

*This would imply that jamil throwings in the pencil holder was 11 nickles and 22 dimes*