a handful of coins is worth $1.50. there are a total of 54 pennies and quartes in the hand
To solve this problem, we can set up a system of equations.
Let's assume the number of pennies in the hand is represented by 'p', and the number of quarters is represented by 'q'.
We are given two pieces of information:
1. The total value of the coins is $1.50. We can represent this information as the equation: 0.01p + 0.25q = 1.50 (since the value of a penny is $0.01 and the value of a quarter is $0.25).
2. The total number of coins is 54. We can represent this information as the equation: p + q = 54.
Now, we can solve this system of equations to find the values of 'p' and 'q'.
1. Simplify the second equation by subtracting 'p' from both sides: q = 54 - p.
2. Substitute the value of 'q' in the first equation: 0.01p + 0.25(54 - p) = 1.50.
3. Simplify the equation: 0.01p + 13.5 - 0.25p = 1.50.
4. Combine like terms: 13.5 - 0.24p = 1.50.
5. Subtract 13.5 from both sides: -0.24p = -12.
6. Divide both sides by -0.24: p = 50.
Now that we know the value of 'p', we can substitute it back into the second equation to find the value of 'q'.
7. Substitute p = 50 into p + q = 54: 50 + q = 54.
8. Subtract 50 from both sides: q = 4.
Therefore, there are 50 pennies and 4 quarters in the hand.