Question 141777
Let x=number of nickels
And let y=number of dimes

Now we are told:

x+y=46-------------------------------------------eq1

and($ understood)
0.05x+0.25y=3.10-------------------------------------eq2

Multiply eq1 by 0.05

0.05x+0.05y=2.3------------------------eq1a

Subtract eq1a from eq2

0.20y=0.80  divide both sides by 0.20
y=4--------------------------------------number of quarters

Substitute y=4 into eq1
x+4=46  subtract 4 from each side

x+4-4=46-4  collect like terms

x=42-----------------------------number of nickels

CK
42+4=46
46=46
and
4*0.25+42*0.05=3.10
1.00+2.10=3.10
3.10=3.10

Another way to solve this problem using 1 unknown:

Let x=number of nickels
Then 46-x=number of quarters
0.05x+0.25(46-x)=3.10   get rid of parens
0.05x+11.50-0.25x=3.10  subtract 11.50 from each side

0.05x+11.50-11.50-0.25x=3.10-11.50  collect like terms

-0.20x=-8.40  divide both sides by -0.20
x=42--------------------------------------------number of nickels

46-42=4--------------------------------------number of quarters


Hope this helps----ptaylor