To determine which graph and equation represent the amount of flour left in the bin after baking [tex]$c$[/tex] cakes, let's analyze step by step.
1. Identify the initial amount of flour and the amount used per cake:
- The baker starts with 30 cups of flour.
- Each cake requires 1.5 cups of flour.
2. Develop an equation based on the initial amount and usage per cake:
- Let [tex]$F$[/tex] represent the amount of flour left in the bin after baking [tex]$c$[/tex] cakes.
- Every time a cake is baked, the amount of flour decreases by 1.5 cups.
We can express this relationship with the equation:
[tex]\[
F = 30 - 1.5c
\][/tex]
Here:
- [tex]$F$[/tex] represents the flour left.
- [tex]$30$[/tex] is the initial amount of flour.
- [tex]$1.5c$[/tex] represents the total flour used for [tex]$c$[/tex] cakes.
3. Verifying the equation in the provided options:
The given options for the equation are:
- [tex]\(F = 1.5 - 30c\)[/tex]
- [tex]\(F = 1.5c - 30\)[/tex]
- [tex]\(F = 30 - 1.5c\)[/tex]
- [tex]\(F = (30 - 1.5)c\)[/tex]
Observing these options:
- [tex]\(F = 1.5 - 30c\)[/tex]: This equation does not correctly represent the scenario. Here, 1.5 should represent the amount of flour used per cake, and 30 should be the initial amount.
- [tex]\(F = 1.5c - 30\)[/tex]: This equation suggests that 30 is being subtracted from flour used, which contradicts the scenario. It also suggests the flour increases with the number of cakes baked.
- [tex]\(F = 30 - 1.5c\)[/tex]: This correctly represents the initial amount of flour minus the amount used per number of cakes baked.
- [tex]\(F = (30 - 1.5)c\)[/tex]: This implies that the flour used per cake changes, which is not accurate here.
4. Choose the correct equation:
The correct equation is:
[tex]\[
F = 30 - 1.5c
\][/tex]
Thus, the equation that represents the amount of flour left in the bin, [tex]$F$[/tex], after baking [tex]$c$[/tex] cakes is: [tex]\(F = 30 - 1.5c\)[/tex].
To graph this equation, you would typically plot [tex]$F$[/tex] on the y-axis and [tex]$c$[/tex] on the x-axis. Starting at [tex]\(F = 30\)[/tex] when [tex]$c = 0$[/tex], the graph would have a negative slope of -1.5 indicating that for each cake baked, the amount of flour decreases by 1.5 cups.
