The cost of 18 small chocolate cakes is the same as the cost of 7 large chocolate cakes. Find the cost of a small chocolate cake.
Answer (2)
Define 's' as the cost of a small cake and 'l' as the cost of a large cake.
Write the equation: 18 s = 7 l .
Express the cost of a large cake in terms of a small cake: l = 7 18 s .
Since there is not enough information, we cannot find a numerical value for the cost of a small chocolate cake. The relationship between the cost of a small and large chocolate cake is l = 7 18 s .
Explanation
Problem Analysis Let's analyze the given information. We know that the cost of 18 small chocolate cakes is equal to the cost of 7 large chocolate cakes. Our goal is to find the cost of a small chocolate cake.
Define Variables Let's define some variables to represent the unknowns. Let 's' be the cost of a small chocolate cake and 'l' be the cost of a large chocolate cake.
Formulate Equation Now, we can write an equation that represents the given information: 18 s = 7 l
Express Large Cake Cost We want to find the cost of a small chocolate cake, 's'. We can express the cost of a large chocolate cake in terms of the cost of a small chocolate cake: l = 7 18 s
Limitations and Conclusion Since we only have one equation and two unknowns, we cannot find a unique numerical value for 's'. We can only express the relationship between the cost of a small and large chocolate cake. Without additional information (like the cost of the large cake or the total cost), we cannot determine the exact cost of a small chocolate cake. Therefore, we can only express the cost of the large cake in terms of the small cake.
Final Answer Therefore, we cannot find a numerical value for the cost of a small chocolate cake.
Examples
Imagine you're baking cakes for a school fundraiser. You know that selling 18 small cakes brings in the same amount of money as selling 7 large cakes. This problem helps you understand the relationship between the prices of the two sizes, so you can price them fairly and maximize your fundraising efforts. Understanding the ratio between the prices allows you to make informed decisions about how many of each size to bake and sell.
We cannot determine the exact cost of a small chocolate cake because we do not have enough information. The relationship between the cost of small and large chocolate cakes is defined by the equation 18 s = 7 l , which leads to l = 7 18 s . Therefore, we can express the cost of a large cake in terms of a small cake but not find a specific value for 's'.
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