You have 85 cents made up of nickels (5 cents) and (25 cents). You only have 9 coins. How many quarters and nickels do you have?
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If you have
x
nickels and
9
coins in total, therefore you must have
9
−
x
quarters.
Then determine the unit price of each coin.
Nickels are
5
cents a piece, and quarters are
25
cents a piece.
Now you have to get the total, so multiply the amount by the unit price for both coins.
Nickels:
5
x
Quarters:
25
(
9
−
x
)
Now considering this information, adding them together must add to
85
cents because that is the total amount you have. This gives us the following equation:
5
x
+
25
(
9
−
x
)
=
85
Simplify.
5
x
+
225
−
25
x
=
85
−
20
x
+
225
=
85
−
20
x
=
−
140
x
=
7
This means that you have
7
nickels.
Now knowing this and that you have
9
total coins, you have to do
9
−
7
to get
2
, the amount of quarters you have.
So this is why you have
7
nickels and
2
quarters.
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