2) Once Grady, Sophia and Ella returned home, a careful process of sorting and trading candy began. The kids agreed on a barter system: 1 piece of bubble gum is worth 4 candy corns, 1 lollipop is worth 3 pieces of bubble gum, and 1 candy bar is worth 2 lollipops. If candy bars are sold in bags of 35 bars and candy corns are sold in bags of 80 candy corns, how many bags of candy corn are equal to a bag of candy bars? Express your answer as a decimal to the nearest tenth.

1 bag of CB = 10.5 bags of candy corns

Step-by-step explanation:

The kids have an agreement on how to trade their goods:

1 piece of bubble gum (BG) = 4 candy corns (CC)

1 lollipop (LP) = 3 pieces of bubble gum (BG)

1 candy bar (CB) = 2 lollypops (LP)

This last equivalence will be expanded by using back the other agreements:

1 CB = 2 LP

But since:

1 LP =3 BG, then

1 CB = 2 * 3 GB = 6 GB

Also 1 GB = 4 CC, thus:

1 CB = 6 * 4 CC = 24 CC

1 candy bar = 24 candy corns

If we multiply by 35:

35 candy bars = 35 * 24 candy corns

But 35 candy bars = 1 bag of CB, thus

1 bag of CB = 35 * 24 candy corns

If we now divide by 80:

1 bag of CB = 35 * 24 / 80 bags of candy corns

Operating:

1 bag of CB = 10.5 bags of candy corns