132k views
5 votes
The value of Bianca rolls of coins is $136.00 of Pennie's and dimes come in rolls of 50 coins each, and nickels and quarters come in rolls of 40 coins each, which of these combinations could Bianca have

The value of Bianca rolls of coins is $136.00 of Pennie's and dimes come in rolls-example-1
User Kristian
by
8.2k points

1 Answer

2 votes

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.

User Martin Golpashin
by
8.1k points