Marysia has saved $45.25 in quarters and loonies. If she has 3 quarters fewer than three-fifths the number of loonies, how many coins of each type does Marysia have?
Let the number of loonies be L.
The number of quarters is 3 quarters less than three-fifths the number of loonies, which represents L*3/5 - 3.
Thus, the equation is L*3/5 - 3 = 45.25.
Multiplying through the parentheses, we get 3L/5 - 3 = 45.25.
Multiplying through the equation by 5 gives us 3L - 15 = 226.25.
Adding 15 to both sides gives us 3L = 241.25.
Finally, dividing both sides by 3 gives us L = 80. <<80=80>>Answer: \boxed{80}.
Let's assume that the number of loonies Marysia has is x.
According to the given information, the number of quarters Marysia has is 3 fewer than three-fifths of the number of loonies, which can be written as (3/5)x - 3.
In Canadian currency, a loonie is worth $1 and a quarter is worth $0.25.
So, the total value of the loonies is x dollars and the total value of the quarters is 0.25((3/5)x - 3) dollars.
By adding the values of the loonies and quarters, we can set up the following equation:
x + 0.25((3/5)x - 3) = 45.25
Let's simplify the equation:
x + 0.75x/5 - 0.75 = 45.25
Multiplying by 5 to eliminate the fraction:
5x + 0.75x - 3.75 = 226.25
Combining like terms:
5.75x - 3.75 = 226.25
Adding 3.75 to both sides of the equation:
5.75x = 230
Dividing by 5.75 to isolate x:
x = 40
Therefore, Marysia has 40 loonies.
Plugging in the value of x into the equation (3/5)x - 3, we can find the number of quarters:
(3/5)(40) - 3 = 24 - 3 = 21
Therefore, Marysia has 21 quarters.
In conclusion, Marysia has 40 loonies and 21 quarters.
To solve this problem, we can set up a system of equations. Let's say the number of quarters Marysia has is q, and the number of loonies she has is l.
We are given that Marysia has saved $45.25 in quarters and loonies. Since a quarter is worth $0.25 and a loonie is worth $1.00, we can write the following equation:
0.25q + 1.00l = 45.25
We are also given that Marysia has 3 quarters fewer than three-fifths the number of loonies. Mathematically, this can be expressed as:
q = (3/5)l - 3
Now we have a system of equations:
0.25q + 1.00l = 45.25
q = (3/5)l - 3
We can solve this system of equations using substitution or elimination:
Let's use substitution:
Substituting the value of q from the second equation into the first equation, we get:
0.25((3/5)l - 3) + 1.00l = 45.25
Simplifying this equation, we have:
0.75l - 0.75 + 1.00l = 45.25
1.75l = 45.25 + 0.75
1.75l = 46
l = 46 / 1.75
l ≈ 26.29
Since the number of loonies must be a whole number, Marysia has approximately 26 loonies.
Now we can substitute this value of l back into the equation for q:
q = (3/5)l - 3
q = (3/5)(26) - 3
q ≈ 15.6 - 3
q ≈ 12.6
Since the number of quarters must be a whole number, Marysia has approximately 12 quarters.
Therefore, Marysia has approximately 12 quarters and 26 loonies.