Moussa and Nicole are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Moussa mixes $4$ cups of dough with $1$ quarter-cup of chocolate chips and Nicole mixes $6$ cups of dough with $1$ quarter-cup of chocolate chips. Whose cookies will be more chocolaty? $\newline$ Moussa's cookies will be more chocolaty. $\newline$ Nicole's cookies will be more chocolaty. $\newline$ The two sets of cookies will be equally chocolaty.

Full solution

Q. Moussa and Nicole are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Moussa mixes

4

cups of dough with

1

quarter-cup of chocolate chips and Nicole mixes

6

cups of dough with

1

quarter-cup of chocolate chips. Whose cookies will be more chocolaty?

\newline

Moussa's cookies will be more chocolaty.

\newline

Nicole's cookies will be more chocolaty.

\newline

The two sets of cookies will be equally chocolaty.

Calculate Ratio for Moussa: Determine the ratio of chocolate chips to cookie dough for Moussa. Moussa uses $1$ quarter-cup of chocolate chips for $4$ cups of dough. The ratio is $\frac{1}{4}$ cup of chocolate chips to $4$ cups of dough. To simplify, divide both the numerator and the denominator by $4$ . $\frac{1}{4} \div 4 = \frac{1}{16}$ (chocolate chips to dough ratio for Moussa).
Calculate Ratio for Nicole: Determine the ratio of chocolate chips to cookie dough for Nicole. Nicole uses $1$ quarter-cup of chocolate chips for $6$ cups of dough. The ratio is $\frac{1}{4}$ cup of chocolate chips to $6$ cups of dough. To simplify, divide both the numerator and the denominator by $4$ . $\frac{1}{4} \div 6 = \frac{1}{24}$ (chocolate chips to dough ratio for Nicole).
Compare Ratios: Compare the ratios to determine whose cookies will be more chocolaty. $\newline$ Moussa's ratio is $\frac{1}{16}$ and Nicole's ratio is $\frac{1}{24}$ . $\newline$ A smaller denominator in a fraction means a larger value when the numerator is the same. $\newline$ Therefore, $\frac{1}{16}$ is greater than $\frac{1}{24}$ . $\newline$ This means Moussa's cookies will have a higher concentration of chocolate chips compared to Nicole's.
Conclude Comparison: Conclude which set of cookies will be more chocolaty. Since Moussa's ratio of chocolate chips to dough is higher than Nicole's, Moussa's cookies will be more chocolaty.