Question

emma was given 5 seashells. each week she collected 3 more. let w be the number of weeks emma collects seashells and s be the number of seashells she has total. which variable is independent and which is dependent?
write an equation to model the relationship, and make a table to show how many seashells she has from week 4 to week 10.

Explanation:

Step1: Identify independent/dependent vars

Independent: $w$ (weeks, controls total shells). Dependent: $s$ (total shells, depends on $w$).

Step2: Derive the relationship equation

Start with 5 shells, add 3 per week:
$$s = 3w + 5$$

Step3: Calculate $s$ for weeks 4-10

For $w=4$: $s=3(4)+5=17$
For $w=5$: $s=3(5)+5=20$
For $w=6$: $s=3(6)+5=23$
For $w=7$: $s=3(7)+5=26$
For $w=8$: $s=3(8)+5=29$
For $w=9$: $s=3(9)+5=32$
For $w=10$: $s=3(10)+5=35$

Answer:

• Independent variable: $w$ (number of weeks collecting seashells)
• Dependent variable: $s$ (total number of seashells)
• Relationship equation: $s = 3w + 5$
• Table of seashells from week 4 to 10:

Number of Weeks ($w$)	Total Seashells ($s$)
5	20
6	23
7	26
8	29
9	32
10	35