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.

Answer 1

Tabitha Tidbits costs $7 per bag, and Figaro Flakes is $5.50 per bag.
You need to set up a system of equations. Use "x" for Tabitha Tidbits and "y" for Figaro Flakes, and let the total cost of each trip equal c. Using the equation ax+by=c, substitute the cost of each trip in for c, and the number of bags for each food for a and b respectively. The two equations will be:
3x+4y=43
3x+6y=54
Isolate x in the first equation and you will get:
x=(43-4y)/3
Substitute the above equation for x into the other equation:
3*((43-4y)/3)+6y=54
Isolate y in this equation, and you will get 11/2, which is 5.5
So the cost of one bag of Figaro Flakes is $5.50
Now substitute this into the equation where you isolated x:
(43-4(5.5))/3
You will get x=7, so a bag of Tabitha Tidbits is $7

Answer 2

One bag of Tabitha Tidbits costs $7 and one bag of Figaro Flakes costs $5.5.

Calculus

Given that one week Carlos bought 3 bags of Tabitha Tidbits and 4 bags of Figaro Flakes for $43.00, and the next week he bought 3 bags of Tabitha Tidbits and 6 bags of Figaro Flakes for $54.00, to figure out the price of one bag of each type of cat food the following calculation must be made:

• 3T + 4F = 43
• 3T + 6F = 54
• 3T = 43 - 4F
• 3T = 54 - 6F
• 43 - 4F = 54 - 6F
• -4F + 6F = 54 - 43
• 2F = 11
• F = 11/2
• F = 5.5
• 3T + 4 x 5.5 = 43
• 3T = 43 - 22
• 3T = 21
• T=21/3
• T = 7

Therefore, one bag of Tabitha Tidbits costs $7 and one bag of Figaro Flakes costs $5.5.

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