Bubble gum comes in packs of 7 pieces and cases of 48 packs. If Tara needs 7,500 pieces for the carnival, how many cases should she order?

7 * 48 = 336 pieces in a case.

7500 / 336 = 22.32 cases

She needs to order 23 cases.

To find out how many cases of bubble gum Tara should order, we first need to calculate the total number of pieces in one case.

Since each pack contains 7 pieces, the total number of pieces in one case is: 7 pieces/pack * 48 packs/case = 336 pieces/case.

Next, we can find the number of cases Tara should order by dividing the total number of pieces she needs by the number of pieces in one case.

Number of cases = Total number of pieces needed / Number of pieces in one case

Number of cases = 7,500 pieces / 336 pieces/case ≈ 22.3214.

Since we cannot have a fraction of a case, Tara should order 23 cases of bubble gum to have enough pieces for the carnival.

To solve this problem, we need to determine how many packs of bubble gum Tara needs and then find out how many cases of those packs will be required.

First, let's calculate the number of packs Tara needs. We know that each pack contains 7 pieces and Tara needs a total of 7,500 pieces. Therefore, we can divide 7,500 by 7 to find the number of packs:

7,500 pieces ÷ 7 pieces per pack = 1,071.43 packs

Since we cannot have a fraction of a pack, we will round up to the nearest whole number because Tara cannot buy a fraction of a pack. Therefore, Tara needs to buy at least 1,072 packs of bubble gum.

Next, we can figure out how many cases of bubble gum Tara should order. We know that each case contains 48 packs. To find the number of cases, we need to divide the total number of packs by the number of packs per case:

1,072 packs ÷ 48 packs per case = 22.33 cases

Again, we cannot have a fraction of a case, so we will round up to the nearest whole number. Therefore, Tara should order at least 23 cases of bubble gum to get a total of 1,072 packs or 7,504 pieces.

In conclusion, Tara should order at least 23 cases of bubble gum for a total of 7,504 pieces.