Answer: 15 nickels and 20 dimes
==========================================================
Work Shown:
n = number of nickels
d = number of dimes
d = 2n-10 since "number of dimes is 10 less than twice the number of nickels"
0.05n = value of all the nickels in dollars
0.10d = value of all the dimes in dollars
0.05n+0.10d = total value in dollars
0.05n+0.10d = 2.75
Multiply all three terms by 100 to move the decimal point over two spots to the right. We get this new updated equation
5n+10d = 275
---------
Now plug in d = 2n-10 and solve for n
5n+10d = 275
5n+10(2n-10) = 275
5n+20n-100 = 275
25n-100 = 275
25n = 275+100
25n = 375
n = 375/25
n = 15
There are 15 nickels.
Use this to find the value of d.
d = 2n-10
d = 2*15-10
d = 30-10
d = 20
There are 20 dimes.
-----------
Check:
5n = 5*15 = 75 cents from just the nickels only
10d = 10*20 = 200 cents from just the dimes only
5n+10d = 75+200 = 275 cents total
275 cents = 275/100 = $2.75
This confirms the answers.