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Stan's cookie recipe makes $24$ cookies and calls for exactly $384$ sprinkles. He is wondering how many sprinkles $(p)$ he will need to make $60$ cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make cookies?

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Solve proportions: word problems

Full solution

Q. Stan's cookie recipe makes

24

cookies and calls for exactly

384

sprinkles. He is wondering how many sprinkles

(p)

he will need to make

60

cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make cookies?

Calculate Sprinkles per Cookie: Determine the number of sprinkles per cookie based on the given recipe. $\newline$ The recipe makes $24$ cookies with $384$ sprinkles, so we calculate the number of sprinkles per cookie. $\newline$ Sprinkles per cookie = Total sprinkles / Number of cookies $\newline$ Sprinkles per cookie = $384 / 24$ $\newline$ Sprinkles per cookie = $16$
Calculate Total Sprinkles Needed: Calculate the total number of sprinkles needed for $60$ cookies. $\newline$ Since each cookie has the same number of sprinkles, we multiply the number of sprinkles per cookie by the total number of cookies Stan wants to make. $\newline$ Total sprinkles needed $=$ Sprinkles per cookie $\times$ Number of cookies to make $\newline$ Total sprinkles needed $= 16 \times 60$ $\newline$ Total sprinkles needed $= 960$

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