Question 156231
Let x=number of dimes
Then x will also equal the number of pennies
And let y=number of quarters

Now we are told that: 

0.01x +0.10x +0.25y=4.37 
0.11x+0.25y=4.37  multiply each term by 100
11x+25y=437--------------------------------------eq1
We are also told that:
2x+y=44 or
y=44-2x-------------------eq2

Substitute y=44-2x from eq2 into eq1

11x+25(44-2x)=437  get rid of parens

11x+1100-50x=437 subtract 1100 from each side
11x+1100-1100-50x=437-1100  collect like terms
-39x=-663  divide each side by -39
x=17------------------------------number of dimes and also number of pennies

Substitute x=17 into eq2
y=44-2*17= 10-----------------------number of quarters

CK
2*17+10=44
44=44
and
0.25*10+0.01*17+0.10*17=4.37
2.50+0.17+1.7=4.37
4.37=4.37


Hope this helps--ptaylor