Reed is buying bacon and eggs to serve at a breakfast fundraiser. A dozen eggs cost $2.04 and a pack of bacon costs $4.25. He knows that he must buy at least 5 dozen eggs and no more than 10 packs of bacon. Reed has donated $75 to buy all of the supplies for the fundraiser. Which of the following inequalities could be used to create a system of inequalities to solve for the number of packs of bacon and dozens of eggs he buys from the store?(1 point)

Question

Responses

5e+10b≥75
5
𝑒
+
10
𝑏
≥
75
, e≥5
𝑒
≥
5
, b≤10
𝑏
≤
10
5 e plus 10 b greater-than-or-equal-to 75 , e greater-than-or-equal-to 5 , b less-than-or-equal-to 10

2.04e+4.25b≤10
2.04
𝑒
+
4.25
𝑏
≤
10
, e≥5
𝑒
≥
5
, b≤10
𝑏
≤
10
2.04 e plus 4.25 b less-than-or-equal-to 10 , e greater-than-or-equal-to 5 , b less-than-or-equal-to 10

2.04e+4.25b≤75
2.04
𝑒
+
4.25
𝑏
≤
75
, e≥5
𝑒
≥
5
, b≤10
𝑏
≤
10
2.04 e plus 4.25 b less-than-or-equal-to 75 , e greater-than-or-equal-to 5 , b

Answer 1

To create a system of inequalities to solve for the number of dozens of eggs (e) and packs of bacon (b) Reed buys, we need to consider the following:

1. Cost of purchasing eggs and bacon:

   • The cost for a dozen eggs is $2.04, so for \( e \) dozens, the cost is \( 2.04e \).
   • The cost for a pack of bacon is $4.25, so for \( b \) packs, the cost is \( 4.25b \).
   • The total cost needs to be less than or equal to the budget of $75, which gives us the inequality: \[ 2.04e + 4.25b \leq 75 \]

2. Minimum number of dozen eggs: Reed must buy at least 5 dozen eggs, so we have: \[ e \geq 5 \]

3. Maximum number of packs of bacon: Reed can buy no more than 10 packs of bacon, so this gives us: \[ b \leq 10 \]

Putting all these together, the correct system of inequalities is:

1. Cost inequality: \( 2.04e + 4.25b \leq 75 \)
2. Doughnut constraint: \( e \geq 5 \)
3. Bacon constraint: \( b \leq 10 \)

Thus, the option that matches all these constraints is:

2.04e + 4.25b ≤ 75, e ≥ 5, b ≤ 10.

This corresponds to:

2.04e + 4.25b ≤ 75, e ≥ 5, b ≤ 10.