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Answer :
Sure, let's break down the problem and solve it step-by-step.
### Problem Recap
Jack is ordering two types of items for his Superbowl party:
- Breadsticks, which cost \[tex]$4 each
- Pizzas, which cost \$[/tex]11 each
Jack wants to:
1. Spend at most \[tex]$160.
2. Order a minimum of 20 items in total.
We need to find the two inequalities that represent these conditions.
### Step-by-Step Solution
Condition 1: Budget Constraint
Jack wants to spend at most \$[/tex]160. We can represent this condition mathematically.
If:
- [tex]\( b \)[/tex] is the number of breadsticks
- [tex]\( p \)[/tex] is the number of pizzas
The total spending can be written as:
[tex]\[ 4b + 11p \leq 160 \][/tex]
This is our first inequality.
Condition 2: Minimum Number of Items
Jack also wants to order at least 20 items in total. We can write this condition as:
[tex]\[ b + p \geq 20 \][/tex]
This is our second inequality.
### Conclusion
The two inequalities that correctly represent the conditions given in the problem are:
[tex]\[ 4b + 11p \leq 160 \][/tex]
[tex]\[ b + p \geq 20 \][/tex]
Thus, the correct choices are:
- [tex]\( 4b + 11p \leq 160 \)[/tex]
- [tex]\( b + p \geq 20 \)[/tex]
These inequalities ensure that Jack sticks to his budget and orders a sufficient number of items for his party.
### Problem Recap
Jack is ordering two types of items for his Superbowl party:
- Breadsticks, which cost \[tex]$4 each
- Pizzas, which cost \$[/tex]11 each
Jack wants to:
1. Spend at most \[tex]$160.
2. Order a minimum of 20 items in total.
We need to find the two inequalities that represent these conditions.
### Step-by-Step Solution
Condition 1: Budget Constraint
Jack wants to spend at most \$[/tex]160. We can represent this condition mathematically.
If:
- [tex]\( b \)[/tex] is the number of breadsticks
- [tex]\( p \)[/tex] is the number of pizzas
The total spending can be written as:
[tex]\[ 4b + 11p \leq 160 \][/tex]
This is our first inequality.
Condition 2: Minimum Number of Items
Jack also wants to order at least 20 items in total. We can write this condition as:
[tex]\[ b + p \geq 20 \][/tex]
This is our second inequality.
### Conclusion
The two inequalities that correctly represent the conditions given in the problem are:
[tex]\[ 4b + 11p \leq 160 \][/tex]
[tex]\[ b + p \geq 20 \][/tex]
Thus, the correct choices are:
- [tex]\( 4b + 11p \leq 160 \)[/tex]
- [tex]\( b + p \geq 20 \)[/tex]
These inequalities ensure that Jack sticks to his budget and orders a sufficient number of items for his party.
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