The amount of money in cents in a jar containing d dimes and some nickels and quarters if there are 8 times as many nickels as dimes and 2 times as many quarters as nickels
there is not enough information to determine the total cents
one dime , eight nickels , 16 quarters
two dimes , 16 nickels , 32 quarters
the ratios are the same ... so the total amount cannot be calculated
To find the amount of money in cents in the jar, we need to determine the value of each coin and then calculate the total.
First, let's express the number of nickels and quarters in terms of the number of dimes (d).
Since there are 8 times as many nickels as dimes, we can write the number of nickels as 8d.
Similarly, there are 2 times as many quarters as nickels, so we can write the number of quarters as 2 * 8d = 16d.
Next, we must determine the value of each coin in cents.
- Dimes are worth 10 cents each.
- Nickels are worth 5 cents each.
- Quarters are worth 25 cents each.
Finally, we can calculate the total amount of money in the jar.
The value of the dimes is 10 cents * d dimes = 10d cents.
The value of the nickels is 5 cents * 8d nickels = 40d cents.
The value of the quarters is 25 cents * 16d quarters = 400d cents.
Adding the values of each coin, we find that the total amount of money is 10d + 40d + 400d cents.
Simplifying, we get 450d cents.
Therefore, the amount of money in cents in the jar is 450 times the number of dimes (d).