SOLUTION: Sally has $21.40 in dimes and quaters, for a total of 100 coins.How many of each kind of coins does Sally have? I dont understand this, could someone please help?

Click here to see ALL problems on Linear-systems

Question 120557: Sally has $21.40 in dimes and quaters, for a total of 100 coins.How many of each kind of coins does Sally have?
I dont understand this, could someone please help?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
d = no. of dimes;
q = no. of quarters
:
Translate each statement into a simple equation:
:
"Sally has $21.40 in dimes and quarters,"
.10d + .25q = 21.40
:
for a total of 100 coins."
d + q = 100
d = (100-q); in this form we can use it for substitution
:
How many of each kind of coins does Sally have?
:
Substitute (100-q) for d in the $value equation and solve for q
:
.10(100-q) + .25q = 21.40
:
10 - .10q + .25q = 21.40
:
.15q = 21.40 - 10
:
.15q = 11.40
:
q = 11.40/.15
:
q = 76 quarters
:
Remember we said d = 100 - q
d = 100 - 76
d = 24 dimes
:
:
Check our solutions in the value equation:
.10(24) + .25(76) =
2.4 + 19 = 21.40 as expected
:
Did I make this understandable to you? Let me know.