Natalie sliced 5 cakes. Each chocolate cake had 5 slices and each lemon cake had 10 slices. If Natalie made 40 slices in total, how many of each type of cake did she slice?
Question
Natalie sliced 5 cakes. Each chocolate cake had 5 slices and each lemon cake had 10 slices. If Natalie made 40 slices in total, how many of each type of cake did she slice?
Solution
Let's denote the number of chocolate cakes as C and the number of lemon cakes as L.
From the problem, we know two things:
- C + L = 5 (Natalie sliced 5 cakes in total)
- 5C + 10L = 40 (Each chocolate cake had 5 slices and each lemon cake had 10 slices, and Natalie made 40 slices in total)
We can solve these equations step by step:
First, let's multiply the first equation by 5:
5C + 5L = 25
Now, let's subtract this new equation from the second equation:
5C + 10L - (5C + 5L) = 40 - 25 5L = 15
So, L = 15 / 5 = 3. Natalie sliced 3 lemon cakes.
Substitute L = 3 into the first equation:
C + 3 = 5 C = 5 - 3 = 2. Natalie sliced 2 chocolate cakes.
So, Natalie sliced 2 chocolate cakes and 3 lemon cakes.
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