How to Solve a Cost Problem Involving Granola Bars and Water Bottles

What is the cost of each item if 3 granola bars and 2 bottles of water cost $7, and 2 granola bars and 1 bottle of water cost $4? A granola bar costs $1, and a bottle of water costs $2.

Solving the Cost Problem:

To find the cost of each item, let's assign variables to represent the cost of a granola bar and a bottle of water. Let's say x represents the cost of a granola bar and y represents the cost of a bottle of water. From the given information, we can create two equations. The first equation represents the cost of 3 granola bars and 2 bottles of water, which equals $7. This can be written as 3x + 2y = 7. The second equation represents the cost of 2 granola bars and 1 bottle of water, which equals $4. This can be written as 2x + y = 4.

To solve these equations, we can use a method called elimination. By multiplying the second equation by 2, we get 4x + 2y = 8. Now, we can subtract the first equation from the second equation: (4x + 2y) - (3x + 2y) = 8 - 7. Simplifying, we get x = 1. Substituting the value of x into either of the original equations, we can solve for y. Let's use the second equation: 2(1) + y = 4. Simplifying, we get y = 2.

Therefore, a granola bar costs $1, and a bottle of water costs $2. Hence, the correct answer is B. A granola bar costs $1, and a bottle of water costs $2.

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