We know there are 26 coins in total.
Some of the coins are quarters, which we can assign a variable, lets say “q”
“q” represents the total number of quarters
But what about the remaining coins?
If we have 26 coins, and q of them are quarters, then 26-q must be silver dollars.
Since we know your friend has q quarters, then the value of the quarters must equal…
25 x q = 25q cents from quarters
Since e now know an expression for the value of the quarters, we need to find an xpression for the value of the silver dollars.
We said the amount of silver dollars are equal to 26-q...
What is an expression for the total value?
Lets consider converting the silver dollars into cents...
So $1.00= 100 cents
Therefore, since he has 26-q dollars, he has 100(26-q) cents from the silver dollars...
We know he has seventeen dollars in total (which will soon be yours)
Lets convert the dollars to cents, since that is what we are working with
$ 17.00 = 1700 cents
Part of which is from the quarters and part of which is from the silver dollars
The total value comes from adding the value of the quarters and the value of the silver dollars
25q + 100(26-q) = 1700
25q + 100(26-q) = 1700
25q + 2600 – 100q = 1700
-75q + 2600 = 1700
-75q = -900
q = 12
In other words, 12 of the coins are quarters. Since the total number of coins is 26, we know there are
26-12 = 14 silver dollars.
Some of the coins are quarters, which we can assign a variable, lets say “q”
“q” represents the total number of quarters
But what about the remaining coins?
If we have 26 coins, and q of them are quarters, then 26-q must be silver dollars.
Since we know your friend has q quarters, then the value of the quarters must equal…
25 x q = 25q cents from quarters
Since e now know an expression for the value of the quarters, we need to find an xpression for the value of the silver dollars.
We said the amount of silver dollars are equal to 26-q...
What is an expression for the total value?
Lets consider converting the silver dollars into cents...
So $1.00= 100 cents
Therefore, since he has 26-q dollars, he has 100(26-q) cents from the silver dollars...
We know he has seventeen dollars in total (which will soon be yours)
Lets convert the dollars to cents, since that is what we are working with
$ 17.00 = 1700 cents
Part of which is from the quarters and part of which is from the silver dollars
The total value comes from adding the value of the quarters and the value of the silver dollars
25q + 100(26-q) = 1700
25q + 100(26-q) = 1700
25q + 2600 – 100q = 1700
-75q + 2600 = 1700
-75q = -900
q = 12
In other words, 12 of the coins are quarters. Since the total number of coins is 26, we know there are
26-12 = 14 silver dollars.