David has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $298.79.
He buys 3 bicycle reflectors for $8.13 each and a pair of bike gloves for $21.79.
He plans to spend some or all of the money he has left to buy new biking outfits for $79.43 each.
Which inequality can be used to determine xx, the maximum number of outfits David can purchase while staying within his budget?
Let's set up the inequality. The total amount David spends on the bicycle, reflectors, gloves, and outfits cannot exceed the amount he has, which is $540.
So, we need to subtract the cost of the bicycle, reflectors, and gloves from the total amount he has, and then divide it by the cost of each outfit to determine the maximum number of outfits he can purchase.
Let's denote the maximum number of outfits as xx.
First, we subtract the cost of the bicycle, reflectors, and gloves from the total amount David has:
$540 - $298.79 - 3($8.13) - $21.79 = $540 - $298.79 - $24.39 - $21.79 = $195.03.
Next, we divide this amount by the cost of each outfit in order to determine the maximum number of outfits David can purchase:
$195.03 / $79.43 ≤ x.
Simplifying the inequality, we get:
2.45936 ≤ x.
Therefore, the inequality that can be used is:
x ≥ 2.45936 (rounded up to 3 because we can't buy a fraction of an outfit).
So, the maximum number of outfits David can purchase while staying within his budget is 3.