Carlos and Alexandra are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Carlos mixes $4$ cups of dough with $5$ quarter-cups of chocolate chips and Alexandra mixes $4$ cups of dough with $1$ quarter-cup of chocolate chips. Whose cookies will be doughier? $\newline$ Carlos's cookies will be doughier. $\newline$ Alexandra's cookies will be doughier. $\newline$ The two sets of cookies will be equally doughy.

Full solution

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

4

cups of dough with

5

quarter-cups of chocolate chips and Alexandra mixes

4

cups of dough with

1

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

\newline

Carlos's cookies will be doughier.

\newline

Alexandra's cookies will be doughier.

\newline

The two sets of cookies will be equally doughy.

Calculate Ratio for Carlos: Calculate the ratio of dough to chocolate chips for Carlos's cookies. $\newline$ Carlos uses $4$ cups of dough and $5$ quarter-cups of chocolate chips. $\newline$ Since there are $4$ quarter-cups in a cup, we can convert $5$ quarter-cups to cups by dividing by $4$ . $\newline$ $5$ quarter-cups $/$ $4 = 1.25$ cups of chocolate chips. $\newline$ Ratio of dough to chocolate chips for Carlos = $4$ cups dough $/$ $5$ $0$ cups chocolate chips.
Calculate Ratio for Alexandra: Calculate the ratio of dough to chocolate chips for Alexandra's cookies. Alexandra uses $4$ cups of dough and $1$ quarter-cup of chocolate chips. Since there are $4$ quarter-cups in a cup, we can convert $1$ quarter-cup to cups by dividing by $4$ . $1$ quarter-cup $/$ $4 = 0.25$ cups of chocolate chips. Ratio of dough to chocolate chips for Alexandra = $4$ cups dough $/$ $1$ $0$ cups chocolate chips.
Compare Ratios: Compare the ratios to determine which cookies will be doughier. $\newline$ Carlos's ratio: $\frac{4 \text{ cups dough}}{1.25 \text{ cups chocolate chips}} = 3.2 \text{ cups dough per cup of chocolate chips}.$ $\newline$ Alexandra's ratio: $\frac{4 \text{ cups dough}}{0.25 \text{ cups chocolate chips}} = 16 \text{ cups dough per cup of chocolate chips}.$ $\newline$ Since Alexandra's ratio of dough to chocolate chips is higher, her cookies will be doughier.