a. Susan has $2.40 in nickels, dimes and quarters. She has two more dimes than nickels and four more quarters than nickels. How many types of each coin does Susan have?
Let's start by setting up equations to represent the given information.
Let's say Susan has x nickels. Since she has two more dimes than nickels, she has x + 2 dimes. And since she has four more quarters than nickels, she has x + 4 quarters.
Next, let's calculate the value of each coin.
The value of x nickels is 0.05x dollars.
The value of x + 2 dimes is 0.10(x + 2) dollars.
The value of x + 4 quarters is 0.25(x + 4) dollars.
Since Susan has a total of $2.40, the equation becomes:
0.05x + 0.10(x + 2) + 0.25(x + 4) = 2.40
Simplifying the equation:
0.05x + 0.10x + 0.20 + 0.25x + 1 = 2.40
Combining like terms:
0.40x + 1.20 = 2.40
Subtracting 1.20 from both sides:
0.40x = 1.20
Dividing by 0.40:
x = 3
Therefore, Susan has 3 nickels.
She has 3 + 2 = 5 dimes.
And she has 3 + 4 = 7 quarters.