Barbara has $4.40 worth of change in nickels and dimes. If she has 2 times as many nickels as dimes, how many of each type of coin does she have?
44n. 22d
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and follow the method
To solve this problem, we can set up a system of equations that represents the given information.
Let's assume that the number of dimes Barbara has is represented by 'x', and the number of nickels is represented by 'y'.
From the given information, we know that the total value of the coins is $4.40. In terms of cents, this is equal to 440 cents.
The value of each dime is 10 cents, so the total value of the dimes is 10x.
The value of each nickel is 5 cents, so the total value of the nickels is 5y.
Since we know that Barbara has 2 times as many nickels as dimes, we can write the equation:
y = 2x
Also, we know that the total value of the coins is $4.40, so we can write another equation:
10x + 5y = 440
Now we have a system of two equations:
y = 2x
10x + 5y = 440
To solve this system, we can substitute the value of 'y' from the first equation into the second equation:
10x + 5(2x) = 440
10x + 10x = 440
20x = 440
x = 22
Now that we have the value of 'x', we can substitute it back into the first equation to find the value of 'y':
y = 2(22)
y = 44
Therefore, Barbara has 22 dimes and 44 nickels.