Evan has $580 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 $396.95.
He buys 4 bicycle reflectors for $7.40 each and a pair of bike gloves for $22.94.
He plans to spend some or all of the money he has left to buy new biking outfits for $42.10 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Evan can purchase while staying within his budget.
The total cost of the bicycle reflectors is 4 * $7.40 = $<<4*7.40=29.60>>29.60.
The total cost of the biking outfits is x * $42.10.
The total cost of the items Evan buys is $396.95 + $22.94 + $29.60 + x * $42.10.
Evan's budget is $580, so the inequality is:
$396.95 + $22.94 + $29.60 + x * $42.10 ≤ $580.
Simplifying the inequality, we get:
$449.49 + x * $42.10 ≤ $580.
Subtracting $449.49 from both sides, we get:
x * $42.10 ≤ $580 - $449.49.
x * $42.10 ≤ $130.51.
Dividing both sides by $42.10, we get:
x ≤ $130.51 / $42.10.
x ≤ 3.10.
Therefore, the number of outfits Evan can purchase while staying within his budget is x ≤ 3.
whats the inequality
The inequality is:
396.95 + 22.94 + 29.60 + 42.10x ≤ 580
where x represents the number of outfits Evan can purchase.
Let's assume that Evan can buy x biking outfits. The amount left after purchasing the bicycle, reflectors, gloves, and x outfits will be within his budget.
The total cost of the bicycle, reflectors, gloves, and x outfits can be calculated as:
$396.95 + (4 * $7.40) + $22.94 + (x * $42.10)
To ensure that the total cost is within his budget of $580, we can set up the following inequality:
$396.95 + (4 * $7.40) + $22.94 + (x * $42.10) ≤ $580
Simplifying the expression further:
$396.95 + $29.60 + $22.94 + $42.10x ≤ $580
Combining like terms:
$449.49 + $42.10x ≤ $580
Now, subtracting $449.49 from both sides:
$42.10x ≤ $580 - $449.49
Simplifying:
$42.10x ≤ $130.51
Finally, divide both sides of the inequality by $42.10:
x ≤ $130.51 / $42.10
Simplifying:
x ≤ 3.09715891
Since we can't have a fraction of an outfit, we round down to the nearest whole number:
x ≤ 3
Therefore, Evan can purchase a maximum of 3 biking outfits while staying within his budget.