Question

1. one week carlos bought 3 bags of tabitha tidbits and 4 bags of figaro flakes for $43.00. the next week he bought 3 bags of tabitha tidbits and 6 bags of figaro flakes for $54.00. based on this information, figure out the price of one bag of each type of cat food. explain your reasoning.

Explanation:

Step1: Define Variables

Let \( x \) be the price of one bag of Tabitha Tidbits (in dollars) and \( y \) be the price of one bag of Figaro Flakes (in dollars).

Step2: Set Up Equations

From the first week: \( 3x + 4y = 43 \)
From the second week: \( 3x + 6y = 54 \)

Step3: Subtract Equations

Subtract the first equation from the second equation:
\( (3x + 6y) - (3x + 4y) = 54 - 43 \)
Simplify: \( 2y = 11 \), so \( y = \frac{11}{2} = 5.5 \)

Step4: Solve for \( x \)

Substitute \( y = 5.5 \) into the first equation: \( 3x + 4(5.5) = 43 \)
\( 3x + 22 = 43 \)
Subtract 22: \( 3x = 21 \), so \( x = 7 \)

Answer:

One bag of Tabitha Tidbits costs \$7.00 and one bag of Figaro Flakes costs \$5.50.