A city park employee collected 600 cents in nickels, dimes, and quarters at the bottom of the wishing well. There were 10 nickels, and a combined total of 25 dimes and quarters. How many dimes and quarters were at the bottom of the well?
For information to non-North American readers, the following coins are worth:
dime = 10 cents
nickel = 5 cents
quarter = 25 cents.
600 cents = 10 nickels and 25 dimes and quarters.
Let D=number of dimes
10(5)+10(D)+25(25-D)=600
Isolate D:
-15D=600-625-50=-75
=>
D=-75/(-15)=5
So number of dimes = 5
number of quarters = 25-5=20
number of nickels = 10 (given)
Check:
5(10)+20(25)+10(5)
=50+500+50
=600 ✓
To find out how many dimes and quarters were at the bottom of the well, we can use the information given.
Let's represent the number of dimes as "d" and the number of quarters as "q".
We know that there are 10 nickels, so the total value of the nickels is 10 * 5 cents = 50 cents.
We also know that the total value of the dimes and quarters is 600 cents.
So, we can set up the following equation:
10*5 + 25*(10+d) = 600
Simplifying the equation, we get:
50 + 250 + 25d = 600
Combining like terms, we have:
300 + 25d = 600
Subtracting 300 from both sides, we get:
25d = 300
Dividing both sides by 25, we find:
d = 12
So, there are 12 dimes at the bottom of the well.
Now, let's substitute the value of d into the equation to find the number of quarters:
25*(10 + 12) = 25*22 = 550
Therefore, there are 12 dimes and 22 quarters at the bottom of the well.