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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

5 answers

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.

The cost (in dollars) of a set is (blank) times the number of marbles in the set.

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.

is that correct

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.