Final answer:
To determine the total number of cupcakes Mrs. Pam baked, we set up an equation using the fractions of vanilla and chocolate cupcakes sold and the number of cupcakes left. By solving this equation for the total number of cupcakes, we can find the answer.
Step-by-step explanation:
The question involves the subject of Mathematics, particularly focusing on the concepts of fractions and basic algebra. Mrs. Pam baked some cupcakes, with 3/7 being vanilla and the rest chocolate. She then sold 1/4 of the vanilla cupcakes and 5/8 of the chocolate cupcakes, and had 150 left. To find how many cupcakes she baked altogether, we will use algebra to solve this problem.
Let x be the total number of cupcakes baked. Therefore, the number of vanilla cupcakes is 3/7 of x and the number of chocolate cupcakes is 4/7 of x (since 1 - 3/7 = 4/7). After selling 1/4 of the vanilla and 5/8 of the chocolate cupcakes, there are:
- Vanilla left: 3/7x - (1/4)(3/7)x = 3/7x*(3/4)
- Chocolate left: 4/7x - (5/8)(4/7)x = 4/7x*(3/8)
The combined remaining cupcakes are 150, which gives us the equation:
3/7x*(3/4) + 4/7x*(3/8) = 150
Solving this equation will yield the total number of cupcakes baked by Mrs. Pam.