Barbara has some dimes and quarters if she has 19 coins worth a total of 2.50 how many of each type of coins does she have
Let's assume Barbara has x dimes and y quarters.
The value of x dimes is 0.10*x and the value of y quarters is 0.25*y.
According to the problem, the total number of coins is 19, so we have the equation: x + y = 19.
The total value of all the coins is given as 2.50, so we have the equation: 0.10*x + 0.25*y = 2.50.
Multiplying the first equation by 0.10, we get 0.10*x + 0.10*y = 1.90.
Now, subtracting this equation from the second equation gives us: 0.10*x + 0.25*y - 0.10*x - 0.10*y = 2.50 - 1.90.
Simplifying this equation gives us: 0.15*y = 0.60.
Dividing both sides by 0.15, we find that y = 4.
Substituting this value into the first equation, we get: x + 4 = 19.
Subtracting 4 from both sides gives us: x = 15.
Therefore, Barbara has 15 dimes and 4 quarters.