Tariq has $640 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 $291.24.
He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52.
He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Tariq can purchase while staying within his budget.
Answer
The inequality that can be used to determine the maximum number of outfits Tariq can purchase while staying within his budget is:
640 - 291.24 - (4 * 19.56) - 16.52 - (50.80 * x) ≥ 0
Simplifying the inequality:
640 - 291.24 - 78.24 - 16.52 - 50.80x ≥ 0
254.00 - 50.80x ≥ 0
To solve for x, we isolate the variable:
50.80x ≤ 254.00
x ≤ 254.00 / 50.80
x ≤ 5
Therefore, Tariq can purchase a maximum of 5 biking outfits while staying within his budget.
The inequality to determine the number of outfits Tariq can purchase while staying within his budget is:
$640 - $291.24 - 4($19.56) - $16.52 - $50.80x ≥ 0
Simplifying the equation, we have:
$640 - $291.24 - $78.24 - $16.52 - $50.80x ≥ 0
$264 - $50.80x ≥ 0
To solve for x, we isolate the variable:
$50.80x ≤ $264
x ≤ $264 / $50.80
x ≤ 5.19685
Since Tariq cannot purchase a fraction of an outfit, he can purchase a maximum of 5 outfits while staying within his budget.