Answer:
the bag contains $10.89.
Explanation:
Let's start by using algebra to represent the number of coins in terms of one variable. Let x be the number of pennies in the bag. Then:
The number of nickels is 4 more than the number of pennies, so there are x + 4 nickels.
The number of dimes is 30% of the total, so there are 0.3 * 50 = 15 dimes.
The number of quarters is the remaining coins: 50 - (x + x + 4 + 15) = 31 - 2x.
To find the total amount of money, we need to multiply the number of each type of coin by its value and add them up. Using the values of the coins:
Pennies: x * $0.01
Nickels: (x + 4) * $0.05
Dimes: 15 * $0.10
Quarters: (31 - 2x) * $0.25
Adding these expressions and simplifying, we get:
Total = 0.01x + 0.05(x + 4) + 0.10(15) + 0.25(31 - 2x)
= 0.01x + 0.05x + 0.20 + 1.50 + 7.75 - 0.50x
= 0.06x + 9.45
Now we need to find x, the number of pennies. We know that 14% of the coins are pennies, so:
0.14 * 50 = 7 = x + (x + 4) + 15 + (31 - 2x)
Solving for x, we get:
7 = 50 - x - 19
x = 24
So there are 24 pennies, 28 nickels, 15 dimes, and 3 quarters in the bag. The total amount of money is:
Total = 0.06(24) + 9.45 = $10.89
Therefore, the bag contains $10.89.