ral sal tal val each have 1.85 in quarters and dimes.No two have the same number of coins together how many quarters do they have
Four people have different number of quarters and dimes.
In order to make $1.85 without nickels, each must have an ODD number of quarters, namely 1,3,5 and 7, and the remainder made up of dimes.
The total number of quarters is therefore
1+3+5+7=16
Well, it looks like Ral, Sal, Tal, and Val have quite the piggy banks! If each of them has a total of $1.85 in quarters and dimes, and no two have the same number of coins together, we can figure out the number of quarters each person has.
Now, let's see. Val probably didn't eat any of his dimes, because that would be quite unusual for someone named Val. So let's assume he has all quarters. That leaves us with $1.85 - $1.00 = $0.85 in quarters.
Now, let's distribute the remaining 85 cents among Ral, Sal, and Tal. Since we want to avoid any duplicates, let's start with the smallest number of quarters possible. If Ral has 1 quarter ($0.25), then we're left with $0.60.
Now, we need to distribute the remaining 60 cents among Sal and Tal. To keep things unique, let's give Sal 3 quarters ($0.75), leaving us with $0.60 - $0.75 = -$0.15. Uh-oh!
It seems we've run into a bit of a problem. The remaining amount is a negative value, meaning that our initial assumption doesn't work. Therefore, it's not possible for Ral, Sal, Tal, and Val to each have $1.85 using only quarters and dimes, without having any duplicates.
But hey, maybe they can switch to a different currency that allows for a more exciting distribution of coins!
Let's solve this step-by-step.
Step 1: Let's assume the number of quarters for each person is q1, q2, q3, and q4 respectively.
Step 2: We're given that each person has 1.85 in quarters and dimes. Since quarters have a value of $0.25, the total value for each person can be written as:
For ral: 0.25*q1 + 0.10*(20-q1) = 1.85
For sal: 0.25*q2 + 0.10*(20-q2) = 1.85
For tal: 0.25*q3 + 0.10*(20-q3) = 1.85
For val: 0.25*q4 + 0.10*(20-q4) = 1.85
Step 3: Solve the equations:
For Ral:
0.25*q1 + 2 - 0.10*q1 = 1.85
0.15*q1 = -0.15
q1 = -1
For Sal:
0.25*q2 + 2 - 0.10*q2 = 1.85
0.15*q2 = -0.15
q2 = -1
For Tal:
0.25*q3 + 2 - 0.10*q3 = 1.85
0.15*q3 = -0.15
q3 = -1
For Val:
0.25*q4 + 2 - 0.10*q4 = 1.85
0.15*q4 = -0.15
q4 = -1
Step 4: Checking the results, we find that the values of q1, q2, q3, and q4 are -1, which is not possible since the number of quarters cannot be negative.
Hence, it is not possible to determine how many quarters each person has based on the given information.
To determine how many quarters they have, we need to start by finding out the possible combinations of quarters and dimes each person can have.
Since each person has $1.85, we can represent the number of quarters as 'q' and the number of dimes as 'd' for each person.
Given that dimes have a value of $0.10 (10 cents) and quarters have a value of $0.25 (25 cents), we can set up the following equations:
Person 1: q₁ * $0.25 + d₁ * $0.10 = $1.85
Person 2: q₂ * $0.25 + d₂ * $0.10 = $1.85
Person 3: q₃ * $0.25 + d₃ * $0.10 = $1.85
To find the possible combinations, we can list out the potential options and check for any duplicates.
1 quarter and 6 dimes
2 quarters and 4 dimes
3 quarters and 2 dimes
4 quarters
Let's check if any of these combinations have the same number of coins for any two people.
For the first option, 1 quarter and 6 dimes, we can evaluate it for each person:
Person 1: 1 * $0.25 + 6 * $0.10 = $0.25 + $0.60 = $0.85
Person 2: 1 * $0.25 + 6 * $0.10 = $0.25 + $0.60 = $0.85
Person 3: 1 * $0.25 + 6 * $0.10 = $0.25 + $0.60 = $0.85
Since all three people have the same total value, this combination is not valid.
We can repeat this process for each of the remaining combinations to see if any of them have the same number of coins for any two people. If we find a combination where no two people have the same number of coins, we can determine how many quarters are in that combination.
For the second option, 2 quarters and 4 dimes:
Person 1: 2 * $0.25 + 4 * $0.10 = $0.50 + $0.40 = $0.90
Person 2: 2 * $0.25 + 4 * $0.10 = $0.50 + $0.40 = $0.90
Person 3: 2 * $0.25 + 4 * $0.10 = $0.50 + $0.40 = $0.90
Once again, all three people have the same total value, so this combination is also not valid.
Moving on to the third option, 3 quarters and 2 dimes:
Person 1: 3 * $0.25 + 2 * $0.10 = $0.75 + $0.20 = $0.95
Person 2: 3 * $0.25 + 2 * $0.10 = $0.75 + $0.20 = $0.95
Person 3: 3 * $0.25 + 2 * $0.10 = $0.75 + $0.20 = $0.95
Again, all three people have the same total value, so this combination is not valid either.
Finally, for the last option, 4 quarters:
Person 1: 4 * $0.25 = $1.00
Person 2: 4 * $0.25 = $1.00
Person 3: 4 * $0.25 = $1.00
Since each person has a different total value and no two people have the same number of coins, the combination of 4 quarters is valid.
Therefore, the answer to the question is that they have 4 quarters in total.