Bianca could have a combination of 6 rolls of pennies, 4 rolls of nickels, 9 rolls of dimes, and 8 rolls of quarters. This combination satisfies the given conditions, resulting in a total value of $136.00, with the respective coin roll sizes taken into account.
Option A is correct.
Let's denote the number of rolls for each coin type as follows: P for pennies, N for nickels, D for dimes, and Q for quarters. The respective roll sizes are 50 coins for pennies and dimes, and 40 coins for nickels and quarters.
The total value of the rolls is given by the sum: 0.01 * 50P + 0.05 * 40N + 0.10 * 50D + 0.25 * 40Q = 136
Simplifying this equation gives: 0.50P + 2.00N + 5.00D + 10.00Q = 136
Bianca is looking for a combination of rolls, so the number of rolls should be a positive integer. It's a Diophantine equation, and one way to approach it is by using trial and error or a systematic approach.
Upon trial and error, one combination that satisfies the equation is P = 6, N = 4, D = 9, Q = 8. Substituting these values into the equation, we get: 0.50(6) + 2.00(4) + 5.00(9) + 10.00(8) = 3 + 8 + 45 + 80 = 136
Therefore, the combination of 6 rolls of pennies, 4 rolls of nickels, 9 rolls of dimes, and 8 rolls of quarters satisfies the given conditions, resulting in a total value of $136.00. This is the answer.