Brenda wants to buy a new car and has a budget of $25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1 to 10, with 10 representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by $5000. She also observes that as the gas-mileage index rises by one unit, the price of the car increases by $2500.a.

Question

Brenda wants to buy a new car and has a budget of $25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1 to 10, with 10 representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by $5000. She also observes that as the gas-mileage index rises by one unit, the price of the car increases by $2500.a.

1. Illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her $25,000 budget. Place gas mileage on the horizontal axis.

Answer 1

assuming that an index of zero means a starting price of $0, then

2500G + 5000S <= 25000
or, dividing everything by 2500,
G + 2S <= 10

Answer 2

To illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her $25,000 budget, we need to determine the possible values of S and G within her budget.

Let's assume that the maximum value for the style index (S) is 10 and the maximum value for the gas mileage index (G) is also 10.

Given that Brenda's budget is $25,000, and for every increase of one unit in the style index, the price of the car increases by $5000, we can calculate the maximum style index she can afford by dividing her budget by the price increase per unit:
Maximum Style Index (MSI) = Budget / Price Increase per Style Unit
MSI = $25,000 / $5000
MSI = 5

Similarly, considering that for every increase of one unit in the gas mileage index, the price of the car increases by $2500, we can calculate the maximum gas mileage index she can afford:
Maximum Gas Mileage Index (MGI) = Budget / Price Increase per Gas Mileage Unit
MGI = $25,000 / $2500
MGI = 10

Now, we plot the combinations of style (S) and gas mileage (G) within these limits on a graph:

Style (S) | Gas Mileage (G)
----------------------------------------------
1 | 10
2 | 9
3 | 8
4 | 7
5 | 6

The graph represents the various combinations of style and gas mileage that fall within Brenda's $25,000 budget. Each point on the graph corresponds to a specific style and gas mileage index combination.

Please note that this is just an example, and the actual graph may vary depending on the specific values and constraints mentioned in the question.