Thank you for visiting Sam buys 3 coffees and 2 muffins for 7 Pat buys 2 coffees and 4 muffins for 8 What is the cost of one coffee. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The cost of one coffee is $1.50 and the cost of one muffin is $1.25.
Explanation:
To solve this problem, we can set up a system of linear equations. Let's define the cost of one coffee as 'C' and the cost of one muffin as 'M'. We can then write two equations based on the information given. The first equation is: 3C + 2M = 7, representing the purchase made by Sam. The second equation is: 2C + 4M = 8, representing the purchase made by Pat.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. Multiply the first equation by 2 and the second equation by 3 to make the coefficients of C in both equations the same. This gives us: 6C + 4M = 14 and 6C + 12M = 24. Subtract the first equation from the second equation to eliminate the C term. We get: 8M = 10, which means the cost of one muffin is $1.25.
Substitute this value of M into either of the original equations to find the cost of one coffee. Using the first equation, we have: 3C + 2(1.25) = 7. Simplifying this equation gives us: 3C + 2.5 = 7. Subtract 2.5 from both sides of the equation to isolate 3C, and then divide by 3 to find the value of C. We get: C = 1.5. Therefore, the cost of one coffee is $1.50.
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