Question
Jim saw a magic trick online that used magnetic marbles. He wants to buy a set of the marbles so he can perform the trick. The marbles are sold in three different-sized sets. A set with 120 marbles costs $78, a set with 160 marbles costs $104, and a set with 220 marbles costs $143.
first set : $78 120 marbles
second set : $104 160 marbles
third set : $143 220 marbles
If they are proportional, fill in the blank with a whole number or a decimal.
Proportional
The cost (in dollars) of a set is
Not proportional
first set : $78 120 marbles
second set : $104 160 marbles
third set : $143 220 marbles
If they are proportional, fill in the blank with a whole number or a decimal.
Proportional
The cost (in dollars) of a set is
Not proportional
Answers
GPT-4o mini
To determine whether the cost of the sets is proportional to the number of marbles in each set, we can calculate the cost per marble for each set.
1. **First set:**
- Cost: $78
- Number of marbles: 120
- Cost per marble: \( \frac{78}{120} = 0.65 \) dollars/marble
2. **Second set:**
- Cost: $104
- Number of marbles: 160
- Cost per marble: \( \frac{104}{160} = 0.65 \) dollars/marble
3. **Third set:**
- Cost: $143
- Number of marbles: 220
- Cost per marble: \( \frac{143}{220} \approx 0.650 \) dollars/marble
Since the cost per marble is the same (approximately $0.65) for all three sets, we conclude that the cost of a set is **proportional** to the number of marbles in each set.
The cost (in dollars) of a set is **proportional.**
1. **First set:**
- Cost: $78
- Number of marbles: 120
- Cost per marble: \( \frac{78}{120} = 0.65 \) dollars/marble
2. **Second set:**
- Cost: $104
- Number of marbles: 160
- Cost per marble: \( \frac{104}{160} = 0.65 \) dollars/marble
3. **Third set:**
- Cost: $143
- Number of marbles: 220
- Cost per marble: \( \frac{143}{220} \approx 0.650 \) dollars/marble
Since the cost per marble is the same (approximately $0.65) for all three sets, we conclude that the cost of a set is **proportional** to the number of marbles in each set.
The cost (in dollars) of a set is **proportional.**
. *+. WHY U GOTTA BE ANONYMOUS I WANNA KNOW .+* .
The cost (in dollars) of a set is (blank) times the number of marbles in the set.
GPT-4o mini
To express the cost (in dollars) of a set as a function of the number of marbles in the set, we can use the cost per marble that we calculated earlier. Since the cost per marble is $0.65, the cost of a set is 0.65 times the number of marbles in the set.
Thus, we can fill in the blank as follows:
The cost (in dollars) of a set is **0.65 times** the number of marbles in the set.
Thus, we can fill in the blank as follows:
The cost (in dollars) of a set is **0.65 times** the number of marbles in the set.
. *+. WHY U GOTTA BE ANONYMOUS I WANNA KNOW .+* .
is that correct
GPT-4o mini
Yes, that is correct. The calculations show that for each set, the cost per marble is approximately $0.65. This establishes a clear linear relationship between the cost of a set and the number of marbles.
So we can accurately say:
The cost (in dollars) of a set is **0.65 times** the number of marbles in the set.
So we can accurately say:
The cost (in dollars) of a set is **0.65 times** the number of marbles in the set.