Audrey has $500 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $295.33.
She buys 3 bicycle reflectors for $17.86 each and a pair of bike gloves for $33.62.
She plans to spend some or all of the money she has left to buy new biking outfits for $55.17 each.
Which inequality can be used to determine oo, the maximum number of outfits Audrey can purchase while staying within her budget?
To determine the maximum number of biking outfits Audrey can purchase, we first have to calculate how much money she has left after purchasing the bicycle, the bicycle reflectors, and the gloves.
Here are her initial purchases:
1. Bicycle: $295.33
2. Three bicycle reflectors: $17.86 each
3. Pair of bike gloves: $33.62
Total spent on reflectors = 3 reflectors * $17.86/reflector
Total spent on reflectors = 3 * $17.86
Total spent on reflectors = $53.58
Now, sum all her expenses so far:
Total spent so far = Bicycle + Total spent on reflectors + Gloves
Total spent so far = $295.33 + $53.58 + $33.62
Total spent so far = $382.53
Next, we need to determine how much money Audrey has left:
Money left = Initial budget - Total spent so far
Money left = $500 - $382.53
Money left = $117.47
Now, she wants to buy outfits that cost $55.17 each. Let's denote the maximum number of outfits she can buy as oo. The amount spent on the outfits will be $55.17 times oo.
The inequality showing the maximum number of outfits she can purchase while staying within her budget is:
$55.17 * oo ≤ $117.47
Where oo is an integer (since she can't buy a fraction of an outfit), and it represents the maximum number of biking outfits Audrey can purchase without exceeding the remaining budget of $117.47.
Answer choices:
A. 382,53 + 55.17o ≤ 500
B. 382,53 + 55.17o ≥ 500
C. 500 ≤ 55.17 (o+382.53)
D. 500 ≥55.17 (o+382.53)
The correct answer is:
A. 382.53 + 55.17o ≤ 500
This inequality represents that the total amount spent ($382.53 on the bicycle, reflectors, and gloves plus $55.17 for each outfit, represented by o) is less than or equal to her budget ($500). This ensures that Audrey does not exceed her spending limit while purchasing the o outfits.
The other inequalities do not correctly represent the scenario described:
B. Suggests that Audrey's total spending on the outfits and other items should be greater than or equal to her budget, which would imply she is allowed to overspend, so this is incorrect.
C. Is structured incorrectly, as it implies that Audrey's budget is less than or equal to the cost of the outfits plus some incorrect, unreasonably high value (the parentheses are incorrectly placed, and the values within do not mathematically translate into a meaningful constraint on spending for the outfits).
D. Similar to option C, this inequality is also structured incorrectly for the given problem. It implies Audrey has a budget greater than or equal to an unreasonably high amount, resulting from the incorrect grouping of terms within the parentheses.
Hence, option A is the accurate representation of the maximum number of outfits Audrey can purchase within her budget, since it keeps her total spending at or below her starting budget of $500. Note that the comma in 382,53 should be a decimal point, so it should be 382.53, to be consistent with the decimal notation used elsewhere.
To determine the maximum number of outfits Audrey can purchase while staying within her budget, we can set up an inequality equation.
First, let's calculate how much Audrey has already spent:
$295.33 (new bicycle) + 3 * $17.86 (reflectors) + $33.62 (bike gloves)
Simplifying, we get:
$295.33 + $53.58 + $33.62 = $382.53
Next, let's calculate how much money Audrey has left:
$500 (initial budget) - $382.53 (amount already spent)
Simplifying, we get:
$500 - $382.53 = $117.47
Now we need to determine the maximum number of outfits Audrey can purchase, each costing $55.17, within the remaining budget of $117.47.
Let's denote the maximum number of outfits as "oo". We can set up the following inequality equation to represent this situation:
$55.17 * oo ≤ $117.47
This equation states that the cost of oo outfits (each costing $55.17) should be less than or equal to the remaining budget of $117.47.
Therefore, the inequality that can be used to determine oo, the maximum number of outfits Audrey can purchase while staying within her budget, is:
$55.17 * oo ≤ $117.47