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A baker has a bin filled with 30 cups of flour. His signature cake requires one and a half cups of flour. Determine which graph and which equation represent the amount of flour in the bin, [tex][tex]$F$[/tex][/tex], after he bakes [tex]$c$[/tex] signature cakes.

Sagot :

GinnyAnsweridn
Sure, let's approach the problem step by step.

1. Initial Amount: The baker starts with a bin containing 30 cups of flour. This is our initial value.

2. Flour Requirement per Cake: Each signature cake requires 1.5 cups of flour to bake.

3. Equation Setup: We want to determine the amount of flour [tex]\(F\)[/tex] remaining in the bin after baking [tex]\(c\)[/tex] number of cakes. Let's denote:
- [tex]\(F\)[/tex] as the amount of flour remaining in the bin.
- [tex]\(c\)[/tex] as the number of cakes baked.

4. Formulating the Equation:
- Initially, there are 30 cups of flour.
- For each cake baked, 1.5 cups of flour is used.
- Therefore, the amount of flour used after baking [tex]\(c\)[/tex] cakes is [tex]\(1.5 \times c\)[/tex].

5. Remaining Flour: To find the remaining flour [tex]\(F\)[/tex], we subtract the total flour used from the initial amount of flour. Thus our equation becomes:
[tex]\[ F = 30 - 1.5c \][/tex]
This equation shows the relationship between the amount of flour remaining [tex]\(F\)[/tex] and the number of cakes baked [tex]\(c\)[/tex].

6. Graph Representation: In a graph, this equation can be represented as a straight line with:
- The y-axis (vertical axis) representing the amount of flour [tex]\(F\)[/tex].
- The x-axis (horizontal axis) representing the number of cakes [tex]\(c\)[/tex].

7. Plotting Key Points:
- Starting Point: When [tex]\(c = 0\)[/tex], no cakes are baked, so the flour is at its initial amount: [tex]\(F = 30\)[/tex].
- Slope: For each additional cake baked (moving 1 unit to the right on the x-axis), the amount of flour decreases by 1.5 cups (moving 1.5 units down on the y-axis).

Thus, the graph will be a downward sloping line starting from (0, 30) and descending with a slope of -1.5.

In summary:
- The equation representing the amount of flour in the bin after baking [tex]\(c\)[/tex] signature cakes is:
[tex]\[ F = 30 - 1.5c \][/tex]
- This equation can be graphically represented by a line with a y-intercept at 30 and a slope of -1.5, reflecting the reduction in flour as more cakes are baked.
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