Question

1. souvenirs valentina is buying hats and t - shirts as souvenirs on her vacation. the hats cost $10 each and the t - shirts cost $15 each. she has $60 to spend on souvenirs. write and graph an inequality that represents this situation.

Explanation:

Step1: Define variables

Let $x$ = number of hats, $y$ = number of T-shirts.

Step2: Set up cost inequality

Total cost ≤ total budget:
$$10x + 15y \leq 60$$

Step3: Simplify the inequality

Divide all terms by 5:
$$2x + 3y \leq 12$$

Step4: Find intercepts for graph

• x-intercept (y=0): $2x=12 \implies x=6$
• y-intercept (x=0): $3y=12 \implies y=4$

Step5: Graph the boundary line

Draw a solid line through (6,0) and (0,4) (solid because ≤ includes equality). Shade the region below the line (since $2x+3y$ must be less than or equal to 12) and only include non-negative integer points (can't buy negative souvenirs).

Answer:

Inequality: $\boldsymbol{10x + 15y \leq 60}$ (or simplified $\boldsymbol{2x + 3y \leq 12}$)
Graph: Solid line connecting (6, 0) and (0, 4), with the region below/left of the line (including non-negative x,y values) shaded.