Mav has $560 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 $425.05.
She buys 4 bicycle reflectors for $15.19 each and a pair of bike gloves for $15.79.
She plans to spend some or all of the money she has left to buy new biking outfits for $29.20 each.
Write and solve an inequality which can be used to determine o, the number of outfits Mav can purchase while staying within her budget.
Let o be the number of outfits Mav can purchase.
The cost of buying the bicycle, reflectors, gloves, and outfits can be calculated as follows:
Bicycle cost: $425.05
Reflectors cost: 4 * $15.19
Gloves cost: $15.79
Outfits cost: o * $29.20
The total cost should be less than or equal to the budget of $560:
$425.05 + 4 * $15.19 + $15.79 + o * $29.20 ≤ $560
Simplifying the inequality:
$425.05 + 4 * $15.19 + $15.79 + $29.20o ≤ $560
$425.05 + $60.76 + $15.79 + $29.20o ≤ $560
$502.60 + $29.20o ≤ $560
To solve for o, we can subtract $502.60 from both sides:
$29.20o ≤ $560 - $502.60
$29.20o ≤ $57.40
Finally, we divide both sides by $29.20:
o ≤ $57.40 / $29.20
o ≤ 1.964
Therefore, Mav can purchase a maximum of 1 outfit while staying within her budget.
what is the inequality and the answer
The inequality is:
$502.60 + $29.20o ≤ $560
The answer is:
o ≤ 1.964
Let's assume that Mav can purchase "o" outfits.
The total amount spent on the bicycle, reflectors, gloves, and outfits should be less than or equal to the amount she has, which is $560.
The total amount spent on the bicycle, reflectors, gloves, and outfits can be calculated as follows:
$425.05 (price of the bicycle) +
4 * $15.19 (price of the reflectors) +
$15.79 (price of the gloves) +
o * $29.20 (price of each outfit)
So the inequality can be written as:
$425.05 + 4 * $15.19 + $15.79 + o * $29.20 ≤ $560
Simplifying this inequality:
$425.05 + $60.76 + $15.79 + $29.20o ≤ $560
$501.60 + $29.20o ≤ $560
Subtracting $501.60 from both sides:
$29.20o ≤ $58.40
Dividing both sides by $29.20 (since it is a positive number):
o ≤ 2
Therefore, the inequality is o ≤ 2. This means Mav can purchase a maximum of 2 outfits while staying within her budget.