Lola has twice as many quarters and half as many nickels as Ellen. Ellen has $6.30 in quarters and nickels and has 6 fewer nickels than quarters. How much money does Lola have?

Provide the answer in terms of quarters and nickels.

To solve this problem, let's use variables to represent the number of quarters and nickels that Ellen has. Let's say Ellen has q quarters and n nickels. From the given information, we know that Ellen has $6.30 in quarters and nickels. Since each quarter is worth $0.25, we can write an equation: 0.25q + 0.05n = 6.30.
We also know that Ellen has 6 less nickels than quarters. We can write the second equation: n = q - 6.
Now, let's solve the system of equations to find the values of q and n. Substituting the value of n from the second equation into the first equation, we get: 0.25q + 0.05(q - 6) = 6.30. Simplifying this equation, we get: 0.30q - 0.30 = 6.30. Solving this equation, we find that q = 24.
Now we can substitute the value of q back into the second equation to find the value of n: n = 24 - 6 = 18. Therefore, Ellen has 24 quarters and 18 nickels.
Since Lola has twice as many quarters as Ellen, Lola has 2 * 24 = 48 quarters. And since Lola has half as many nickels as Ellen, Lola has 1/2 * 18 = 9 nickels. Therefore, Lola has $0.25 * 48 + $0.05 * 9 = $12 + $0.45 = $12.45.

Answered by NormanReedus | 2024-06-24

Lola has twice as many quarters as Ellen and half as many nickels as Ellen. Ellen has $6.30 in quarters and nickels and has 6 fewer nickels than quarters.
Let's start by defining the variables:

Let x be the number of quarters Ellen has.
Then, 2x would be the number of quarters Lola has.
Also, (x-6) would be the number of nickels Ellen has because she has 6 fewer nickels than quarters.
And, (1/2)(x-6) would be the number of nickels Lola has because she has half as many nickels as Ellen.

Now, let's set up the equation:
$6.30 = 0.25x + 0.05[(1/2)(x-6)]
Simplify and solve for x:
$6.30 = 0.25x + 0.025x - 0.15
$6.30 = 0.275x - 0.15
0.275x = $6.30 + 0.15
0.275x = $6.45
x = $6.45 / 0.275 = $23.45
So, Ellen has $23.45 in quarters and Lola has twice as many quarters, which is $23.45 x 2 = $46.90. Therefore, Lola has $46.90.

Answered by qwcat | 2024-06-24

Lola has a total of $11.40, consisting of 44 quarters and 8 nickels. Ellen has 22 quarters and 16 nickels, which forms the basis of the calculation. This was derived through a system of equations based on the relationships between their coins.
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Answered by NormanReedus | 2024-12-22