Sure, let's go through the detailed step-by-step solution to find out the maximum number of outfits Evan can purchase.
1. Initial Budget:
Evan starts with [tex]\(\$ 580\)[/tex].
2. Expenses:
a. He buys a new bicycle for [tex]\(\$ 396.95\)[/tex].
b. He buys 4 bicycle reflectors at [tex]\(\$ 7.40\)[/tex] each.
c. He buys a pair of bike gloves for [tex]\(\$ 22.94\)[/tex].
3. Calculations:
a. Total cost of bicycle reflectors:
[tex]\[
4 \times 7.40 = 29.60
\][/tex]
b. Total amount spent on initial items (bicycle + reflectors + gloves):
[tex]\[
396.95 + 29.60 + 22.94 = 449.49
\][/tex]
c. Remaining amount of money after these purchases:
[tex]\[
580 - 449.49 = 130.51
\][/tex]
4. Determine the number of outfits Evan can buy:
Let [tex]\( x \)[/tex] be the number of outfits Evan can purchase, each costing [tex]\(\$ 42.10\)[/tex].
The inequality that represents this situation is:
[tex]\[
42.10x \leq 130.51
\][/tex]
5. Solve the inequality:
To find [tex]\( x \)[/tex], you divide both sides of the inequality by [tex]\( 42.10 \)[/tex]:
[tex]\[
x \leq \frac{130.51}{42.10} \approx 3.10
\][/tex]
Since [tex]\( x \)[/tex] represents the number of outfits and must be a whole number:
[tex]\[
x \leq 3
\][/tex]
So, Evan can purchase a maximum of 3 biking outfits.
Answer:
Inequality: [tex]\( 42.10x \leq 130.51 \)[/tex]
Maximum number of outfits Evan can purchase: [tex]\( x \leq 3 \)[/tex]
Hence, the maximum number of outfits Evan can buy is 3.
