David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is $15:1$ . He currently has $40$ grams of the spice blend, and he can go buy more if necessary. He wants to make $10$ servings, where each serving has $75$ grams of rice. $\newline$ Overall, David spends $4.50$ dollars on rice. $\newline$ How many servings can David make with the current amount of spice he has? $\newline$ $\square$ servings

Full solution

Q. David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is

15:1

. He currently has

40

grams of the spice blend, and he can go buy more if necessary. He wants to make

10

servings, where each serving has

75

grams of rice.

\newline

Overall, David spends

4.50

dollars on rice.

\newline

How many servings can David make with the current amount of spice he has?

\newline

\square

servings

Calculate Rice Amount: First, let's find out how much rice David needs for one serving. He needs $75$ grams of rice per serving.
Total Rice Calculation: Now, let's calculate the total amount of rice he needs for $10$ servings. That's $75$ grams per serving times $10$ servings, which equals $750$ grams of rice.
Calculate Spice Amount: Since the rice-to-spice ratio is $15:1$ , we can find out how much spice is needed for $750$ grams of rice. For every $15$ grams of rice, we need $1$ gram of spice.
Total Spice Calculation: To find the total spice needed, we divide the total rice by the ratio of rice to spice. So, $750$ grams of rice divided by $15$ equals $50$ grams of spice needed.