Let's break down the problem step-by-step to find the correct answer.
a. Writing the Inequality
You want to determine the total number of cans, which includes those collected in the first two weeks (132 and 146) plus the number collected by the end of the third week (c). You want this total to be at least 325 cans.
The inequality can be set up as follows:
\[ 132 + 146 + c \geq 325 \]
b. Solving for c
Now, we can combine the donations from the first two weeks:
\[ 132 + 146 = 278 \]
Substituting this back into the inequality gives us:
\[ 278 + c \geq 325 \]
To isolate c, we need to subtract 278 from both sides:
\[ c \geq 325 - 278 \] \[ c \geq 47 \]
So, the correct inequality is:
\[ 132 + 146 + c \geq 325; \quad c \geq 47 \]
Choosing the Correct Answer
Based on the options given:
- 132 + 146 + c ≥ 325; c ≥ 47 (This option is correct and matches our findings)
The other options do not correctly represent the situation regarding the number of cans needed.
Final Answers:
- a. \( 132 + 146 + c \geq 325 \)
- b. 47 cans are needed to meet or surpass your goal.