Question
Joshua wants to burn at least 400 calories per day, but no more than 600. He does this by walking and playing basketball. Assuming he burns 4 calories per minute walking, w, and 5 calories per minute spent playing basketball, b, the situation can be modeled using these inequalities:
4w + 5b ≥ 400
4w + 5b ≤ 600
Which are possible solutions for the number of minutes Joshua can participate in each activity? Check the TWO solutions that apply.
60 minutes walking, 80 minutes basketball
50 minutes walking, 50 minutes basketball
40 minutes walking, 40 minutes basketball
70 minutes walking, 60 minutes basketball
20 minutes walking, 60 minutes basketball
60 minutes walking, 20 minutes basketball
4w + 5b ≥ 400
4w + 5b ≤ 600
Which are possible solutions for the number of minutes Joshua can participate in each activity? Check the TWO solutions that apply.
60 minutes walking, 80 minutes basketball
50 minutes walking, 50 minutes basketball
40 minutes walking, 40 minutes basketball
70 minutes walking, 60 minutes basketball
20 minutes walking, 60 minutes basketball
60 minutes walking, 20 minutes basketball
Answers
GPT-4o mini
To determine which options satisfy the calorie-burn inequalities, we will substitute the values of \( w \) (walking) and \( b \) (basketball) into the inequalities:
1. **4w + 5b ≥ 400** (must burn at least 400 calories)
2. **4w + 5b ≤ 600** (must burn no more than 600 calories)
Now, let’s evaluate each option:
1. **60 minutes walking, 80 minutes basketball:**
\[
4(60) + 5(80) = 240 + 400 = 640 \quad (\text{not valid since } 640 > 600)
\]
2. **50 minutes walking, 50 minutes basketball:**
\[
4(50) + 5(50) = 200 + 250 = 450 \quad (\text{valid since } 400 ≤ 450 ≤ 600)
\]
3. **40 minutes walking, 40 minutes basketball:**
\[
4(40) + 5(40) = 160 + 200 = 360 \quad (\text{not valid since } 360 < 400)
\]
4. **70 minutes walking, 60 minutes basketball:**
\[
4(70) + 5(60) = 280 + 300 = 580 \quad (\text{valid since } 400 ≤ 580 ≤ 600)
\]
5. **20 minutes walking, 60 minutes basketball:**
\[
4(20) + 5(60) = 80 + 300 = 380 \quad (\text{not valid since } 380 < 400)
\]
6. **60 minutes walking, 20 minutes basketball:**
\[
4(60) + 5(20) = 240 + 100 = 340 \quad (\text{not valid since } 340 < 400)
\]
### Valid Solutions
The valid options that satisfy both inequalities are:
- **50 minutes walking, 50 minutes basketball**
- **70 minutes walking, 60 minutes basketball**
So the two solutions that apply are:
- **50 minutes walking, 50 minutes basketball**
- **70 minutes walking, 60 minutes basketball**
1. **4w + 5b ≥ 400** (must burn at least 400 calories)
2. **4w + 5b ≤ 600** (must burn no more than 600 calories)
Now, let’s evaluate each option:
1. **60 minutes walking, 80 minutes basketball:**
\[
4(60) + 5(80) = 240 + 400 = 640 \quad (\text{not valid since } 640 > 600)
\]
2. **50 minutes walking, 50 minutes basketball:**
\[
4(50) + 5(50) = 200 + 250 = 450 \quad (\text{valid since } 400 ≤ 450 ≤ 600)
\]
3. **40 minutes walking, 40 minutes basketball:**
\[
4(40) + 5(40) = 160 + 200 = 360 \quad (\text{not valid since } 360 < 400)
\]
4. **70 minutes walking, 60 minutes basketball:**
\[
4(70) + 5(60) = 280 + 300 = 580 \quad (\text{valid since } 400 ≤ 580 ≤ 600)
\]
5. **20 minutes walking, 60 minutes basketball:**
\[
4(20) + 5(60) = 80 + 300 = 380 \quad (\text{not valid since } 380 < 400)
\]
6. **60 minutes walking, 20 minutes basketball:**
\[
4(60) + 5(20) = 240 + 100 = 340 \quad (\text{not valid since } 340 < 400)
\]
### Valid Solutions
The valid options that satisfy both inequalities are:
- **50 minutes walking, 50 minutes basketball**
- **70 minutes walking, 60 minutes basketball**
So the two solutions that apply are:
- **50 minutes walking, 50 minutes basketball**
- **70 minutes walking, 60 minutes basketball**