Question

In one hour, a bakery sold 5 muffins and 9 bagels for total of $25.50. The next hour, the bakery sold 3 muffins and 12 bagels for a total of $28.50. Let m represent the price of one muffin and b represent the cost of one bagel. Draco wrote the following system of linear equations to solve for the cost of each item.

5 m + 9 b = 28.50. 3 m + 12 b = 25.50.

What is Draco’s error?
Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50.
Draco should have written the first equation as 3 m + 9 b = 25.50.
Draco should have written 9b in the second equation and 12b in the first equation.
Draco should have written the second equation as 5 m + 12 b = 28.50.

Answer 1

Draco's error is in the setup of the equations. The first equation should be set equal to the total sales amount of $25.50 from the first hour, and the second equation should be set equal to the total sales amount of $28.50 from the second hour.

So the correct system of equations should be:

1) \(5m + 9b = 25.50\) (for the first hour)
2) \(3m + 12b = 28.50\) (for the second hour)

Therefore, Draco's error is:

**Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50.**