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.

\\(5m + 9b = 28.50\\)
\\(3m + 12b = 25.50\\)

what is dracos 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 \\(3m + 9b = 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 \\(5m + 12b = 28.50\\).

Explanation:

Identify variables and given values

Using the Variable Identification knowledge point

$$
LATEXBLOCK0
$$

Translate first hour scenario

Using the System of Equations Translation knowledge point

$$
LATEXBLOCK1
$$

Translate second hour scenario

Using the System of Equations Translation knowledge point

$$
LATEXBLOCK2
$$

Analyze Draco's system and error

Using the System of Equations Translation knowledge point

$$
LATEXBLOCK3
$$

Answer:

• (A) Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50. (Correct answer)
• (B) Draco should have written the first equation as 3m+9b= 25.50.
• (C) Draco should have written 9b in the second equation and 12b in the first equation.
• (D) Draco should have written the second equation as 5m+12b= 28.50.