My piggy bank has only nickels, dimes, and dollar bills. The ratio of nickels to dimes is 2:3, and the ratio of dimes to dollar bills is 8:1. What is the ratio of coins to dollar bills?
A 40:3
b 16:3
c 13:1
d 5:1
n : d = 2:3 = 16 : 24
d : bills = 8:1 = 24 : 3
n : d : bills = 16:24:3
coins : bills = (16+24) : 3 = 40 : 3
To find the ratio of coins to dollar bills, we need to determine the number of each type of coin.
Let's assume that the number of nickels is 2x, and the number of dimes is 3x (based on the given ratio).
According to the second ratio, the number of dimes (3x) is 8 times the number of dollar bills (8y). Therefore, we can write the equation: 3x = 8y.
To find the values of x and y, we need to find a common multiple of 3 and 8. The least common multiple (LCM) of 3 and 8 is 24.
Let's consider x = 8. If x = 8, then the number of nickels is 2x = 2(8) = 16, and the number of dimes is 3x = 3(8) = 24.
Since the number of dimes is equal to the number of dollar bills (24 = 24), the ratio of coins to dollar bills is 24:24, which simplifies to 1:1.
Therefore, the correct option is d) 5:1.
To find the ratio of coins to dollar bills, we first need to determine the number of nickels, dimes, and dollar bills in the piggy bank.
Let's start by assigning variables to the unknowns:
Let n be the number of nickels, d be the number of dimes, and b be the number of dollar bills.
According to the given information, the ratio of nickels to dimes is 2:3. This can be represented as:
n/d = 2/3
Similarly, the ratio of dimes to dollar bills is 8:1. This can be represented as:
d/b = 8/1
Now, let's solve these equations to find the values of n, d, and b.
From the first equation, we can rewrite it as:
n = (2/3)d
Next, substituting this value of n into the second equation, we have:
(2/3)d/d = 8/1
Simplifying this equation, we get:
2/3 = 8/1
To find the value of d, we multiply both sides of the equation by 3:
(2/3) * 3 = 8/1 * 3
2 = 24/1
2 = 24
However, this equation is inconsistent, which means there is no valid solution. Therefore, we cannot determine the exact values of n, d, and b, and thus we cannot find the ratio of coins to dollar bills.
Given that, we cannot answer the question with the information provided.
Please note that there might be a mistake in the question or missing information that is needed to solve it.