Kadeem has $680 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 $470.65.
He buys 2 bicycle reflectors for $7.87 each and a pair of bike gloves for $15.18.
He plans to spend some or all of the money he has left to buy new biking outfits for $50.98 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Kadeem can purchase while staying within his budget.
Let x be the number of outfits Kadeem can purchase.
The total cost of the outfits is $50.98 * x.
The total amount of money spent so far is $470.65 (for the bicycle) + $7.87 (for the reflectors) + $7.87 (for the reflectors) + $15.18 (for the gloves), which is equal to $502.57.
The remaining amount of money is $680 - $502.57 = $177.43.
Therefore, the inequality is:
50.98x ≤ 177.43
Solving for x:
x ≤ 177.43 / 50.98
x ≤ 3.48
Kadeem can purchase a maximum of 3 outfits while staying within his budget.
Let x be the number of outfits Kadeem can purchase.
The total amount spent on the bicycle, reflectors, gloves, and outfits can be calculated as:
Total cost = (Cost of bicycle) + (Cost of reflectors x 2) + (Cost of gloves) + (Cost of outfit x x)
Total cost = $470.65 + ($7.87 x 2) + $15.18 + ($50.98 x x)
To stay within his budget, the total cost should be less than or equal to the amount Kadeem has, which is $680.
Therefore, the inequality which can be used to determine the maximum number of outfits Kadeem can purchase is:
$470.65 + ($7.87 x 2) + $15.18 + ($50.98 x) ≤ $680
Simplifying the inequality:
$470.65 + $15.74 + $15.18 + ($50.98 x) ≤ $680
$501.57 + ($50.98 x) ≤ $680
Subtracting $501.57 from both sides:
($50.98 x) ≤ $178.43
Dividing both sides by $50.98:
x ≤ 3.5
Therefore, Kadeem can purchase a maximum of 3 outfits while staying within his budget.