Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad. The cost of the fruit salad was $5. This expression was used to represent the amount Jalen should pay: [tex]4 x+2 x+5[/tex]
Based on the expression, the cost of each bottle of water is ______ the cost of each bag of chips.
A. four times
B. two times
C. less than
D. the same as
Answer (2)
The expression 4 x + 2 x + 5 represents the total cost.
4 x represents the cost of 4 bottles of water, and 2 x represents the cost of 2 bags of chips.
Solving the equations 4 w = 4 x and 2 c = 2 x shows that w = x and c = x .
Therefore, the cost of each bottle of water is the same as the cost of each bag of chips.
Explanation
Understanding the Problem Let's analyze the given information. Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad costing $5. The expression representing the total amount Jalen should pay is 4 x + 2 x + 5 . We need to determine the relationship between the cost of each bottle of water and the cost of each bag of chips based on this expression.
Identifying the Costs From the expression 4 x + 2 x + 5 , we can infer that 4 x represents the cost of the 4 bottles of water, and 2 x represents the cost of the 2 bags of chips. Let's denote the cost of each bottle of water as w and the cost of each bag of chips as c .
Formulating Equations We can write the equations: Cost of 4 bottles of water: 4 w = 4 x Cost of 2 bags of chips: 2 c = 2 x
Solving for the Cost of Water and Chips Dividing both sides of the first equation by 4, we get: w = x Dividing both sides of the second equation by 2, we get: c = x
Determining the Relationship Since w = x and c = x , we can conclude that w = c . This means the cost of each bottle of water is the same as the cost of each bag of chips.
Final Answer Therefore, based on the expression, the cost of each bottle of water is the same as the cost of each bag of chips.
Examples
Imagine you're at a school fair where tickets are used to buy items. If 4 bottles of water cost the same as 2 bags of chips, and each ticket represents a certain amount of money, this problem helps you understand that each bottle of water and each bag of chips have the same 'ticket' value. This concept is useful in budgeting, understanding proportional costs, and making fair exchanges.
The expression used by Jalen shows that the cost of each bottle of water is represented by the same variable as the cost of each bag of chips. Thus, the cost of each bottle of water is the same as the cost of each bag of chips. The answer is D) the same as .
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