To find out which graph represents the number of pizzas and sodas Sarah can purchase, we can set up a mathematical model based on her budget.
Let:
- \( p \) = number of pizzas
- \( s \) = number of bottles of soda
From the information provided:
- The cost of one pizza is $8, so the total cost of pizzas is \( 8p \).
- The cost of one bottle of soda is $2, so the total cost of sodas is \( 2s \).
- Sarah's total budget is $40.
The budget constraint can be expressed with the following equation: \[ 8p + 2s \leq 40 \]
We can rearrange this inequality to express \( s \) in terms of \( p \): \[ 2s \leq 40 - 8p \] \[ s \leq 20 - 4p \]
This can be plotted as \( s = 20 - 4p \), which is a linear equation with:
- A y-intercept (when \( p = 0 \)): \( s = 20 \) (which means if she buys 0 pizzas, she can buy 20 sodas).
- An x-intercept (when \( s = 0 \)): Setting \( s = 0 \) in the equation gives: \[ 0 = 20 - 4p \] \[ 4p = 20 \] \[ p = 5 \] (which means if she buys 5 pizzas, she cannot buy any sodas).
This implies that the graph will have a line starting from the y-axis at 20 (sodas) and intersecting the x-axis at 5 (pizzas). The area below this line represents all the combinations of pizzas and sodas that can be purchased without exceeding the budget of $40.
To find the correct graph (W, X, Y, or Z), we need to look for one that:
- Has a line segment from (0, 20) to (5, 0).
- Any points above this line would be combinations that exceed the budget, while points on or below the line are within budget.
Once you identify those details in the options (W, X, Y, Z), you can determine which graph correctly represents Sarah's purchasing options for pizzas and sodas based on her budget.
6 answers