Iman collects quarters,dimes, nickels, and pennies. This morning he took $1.80 from his collection . He counted the coins and found that he had twice as many nickels as dimes . What coins iman have?
Half of 1.80 is 0.90
Take it from there.
There must be some missing info
various solutions are possible
q d n p
1 1 2 125
2 4 8 50
4 3 6 20
6 1 2 0
and lots of others
Hmm. I see what Ms Sue is saying. If there are only nickels and dimes, then each makes up half the total.
To solve this problem, let's go step by step:
1. Let's start by assigning variables to represent the number of each type of coin Iman has. We'll use the following variables:
- Let "q" represent the number of quarters.
- Let "d" represent the number of dimes.
- Let "n" represent the number of nickels.
- Let "p" represent the number of pennies.
2. From the given information, we know that Iman has twice as many nickels as dimes. This can be written as:
n = 2d
3. We also know that Iman has a total of $1.80 in coins. We can write this using the values of each coin:
25q + 10d + 5n + 1p = 180 (since each dollar is equal to 100 cents)
4. Now we can substitute the value of "n" from step 2 into the equation from step 3:
25q + 10d + 5(2d) + 1p = 180
25q + 10d + 10d + 1p = 180
25q + 20d + 1p = 180
5. We can simplify the equation further by dividing all terms by 5:
5q + 4d + 0.2p = 36
Now we have a system of equations to solve:
n = 2d
5q + 4d + 0.2p = 36
To find the solution, we can try different values for "d" and calculate the values of the other variables.
One possible solution is:
- d = 5 (number of dimes)
- n = 2d = 2 * 5 = 10 (number of nickels)
- p can be any value since it doesn't affect the equation. Let's set p = 0 (number of pennies).
Substituting these values into the equation, we can find "q":
5q + 4(5) + 0.2(0) = 36
5q + 20 = 36
5q = 36 - 20
5q = 16
q = 16 / 5
q ≈ 3.2
Since the number of quarters should be a whole number, we can conclude that this solution is not valid.
Please note that there might be other valid combinations of coins that satisfy the given conditions. You can use a similar approach to find additional solutions.