Question

at a farmers market, khalid bought 4 pounds of tomatoes and 7 pounds of broccoli for $28. genevieve bought 5 pounds of tomatoes and 2 pounds of broccoli for $28.50. let \\(t\\) represent the cost of one pound of tomatoes. let \\(b\\) represent the cost of one pound of broccoli. which system of equations will solve for \\(t\\) and \\(b\\)?

\\(4t + 7b = 28.50\\)
\\(5t + 2b = 28.00\\)

\\(5t + 7b = 28.50\\)
\\(4t + 2b = 28.00\\)

\\(4t + 7b = 28.00\\)
\\(5t + 2b = 28.50\\)

\\(5t + 4b = 28.50\\)
\\(7t + 2b = 28.00\\)

Explanation:

Identify the variables

Using the Variable Identification knowledge point

$$
LATEXBLOCK0
$$

Translate Khalid's purchase

Using the Algebraic Translation knowledge point

$$ 4t + 7b = 28.00 $$

Translate Genevieve's purchase

Using the Algebraic Translation knowledge point

$$ 5t + 2b = 28.50 $$

Formulate the system of equations

Using the System of Equations Translation knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(4t + 7b = 28.50\) and \(5t + 2b = 28.00\)
• (B) \(5t + 7b = 28.50\) and \(4t + 2b = 28.00\)
• (C) \(4t + 7b = 28.00\) and \(5t + 2b = 28.50\) (Correct answer)
• (D) \(5t + 4b = 28.50\) and \(7t + 2b = 28.00\)