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Josiah and Bella are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Josiah mixes 4 cups of dough with 3 quarter-cups of chocolate chips and Bella mixes 2 cups of dough with 3 quarter-cups of chocolate chips. Whose cookies will be more chocolaty?
Josiah's cookies will be more chocolaty.
Bella's cookies will be more chocolaty.
The two sets of cookies will be equally chocolaty.

Josiah and Bella are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Josiah mixes 44 cups of dough with 33 quarter-cups of chocolate chips and Bella mixes 22 cups of dough with 33 quarter-cups of chocolate chips. Whose cookies will be more chocolaty?\newlineJosiah's cookies will be more chocolaty.\newlineBella's cookies will be more chocolaty.\newlineThe two sets of cookies will be equally chocolaty.

Full solution

Q. Josiah and Bella are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Josiah mixes 44 cups of dough with 33 quarter-cups of chocolate chips and Bella mixes 22 cups of dough with 33 quarter-cups of chocolate chips. Whose cookies will be more chocolaty?\newlineJosiah's cookies will be more chocolaty.\newlineBella's cookies will be more chocolaty.\newlineThe two sets of cookies will be equally chocolaty.
  1. Calculate Ratio for Josiah: Calculate the ratio of chocolate chips to dough for Josiah.\newlineJosiah uses 33 quarter-cups of chocolate chips for 44 cups of dough.\newlineRatio for Josiah = (3×0.25 cups)/4 cups(3 \times 0.25 \text{ cups}) / 4 \text{ cups}\newlineRatio for Josiah = 0.75 cups/4 cups0.75 \text{ cups} / 4 \text{ cups}\newlineRatio for Josiah = 0.1875 cups0.1875 \text{ cups} of chocolate chips per cup of dough
  2. Calculate Ratio for Bella: Calculate the ratio of chocolate chips to dough for Bella.\newlineBella uses 33 quarter-cups of chocolate chips for 22 cups of dough.\newlineRatio for Bella = (3×0.25 cups)/2 cups(3 \times 0.25 \text{ cups}) / 2 \text{ cups}\newlineRatio for Bella = 0.75 cups/2 cups0.75 \text{ cups} / 2 \text{ cups}\newlineRatio for Bella = 0.375 cups0.375 \text{ cups} of chocolate chips per cup of dough
  3. Compare Ratios: Compare the ratios to determine whose cookies will be more chocolaty.\newlineJosiah's ratio: 0.18750.1875 cups of chocolate chips per cup of dough\newlineBella's ratio: 0.3750.375 cups of chocolate chips per cup of dough\newlineSince Bella's ratio is higher, her cookies will be more chocolaty.

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