Eldar cooks lasagna and spaghetti using pesto sauce. $\newline$ Let $\newline$ $L$ represent the number of batches of lasagna and $\newline$ $S$ represent the number of batches of spaghetti that Eldar can cook with the amount of pesto sauce he has. $\newline$ $0.9L + 0.3S \leq 6$ $\newline$ Eldar cooks $4$ batches of spaghetti. How many batches of lasagna can he cook at most with the remaining pesto sauce? $\newline$ Choose $1$ answer: $\newline$ (A) Eldar can cook $3$ batches of lasagna at most. $\newline$ (B) Eldar can cook $4$ batches of lasagna at most. $\newline$ (C) Eldar can cook $5$ batches of lasagna at most. $\newline$ (D) Eldar can cook $6$ batches of lasagna at most.

Full solution

Q. Eldar cooks lasagna and spaghetti using pesto sauce.

\newline

Let

\newline

L

represent the number of batches of lasagna and

\newline

S

represent the number of batches of spaghetti that Eldar can cook with the amount of pesto sauce he has.

\newline

0.9L + 0.3S \leq 6

\newline

Eldar cooks

4

batches of spaghetti. How many batches of lasagna can he cook at most with the remaining pesto sauce?

\newline

Choose

1

answer:

\newline

(A) Eldar can cook

3

batches of lasagna at most.

\newline

(B) Eldar can cook

4

batches of lasagna at most.

\newline

5

batches of lasagna at most.

\newline

(D) Eldar can cook

6

batches of lasagna at most.

Understand the inequality: Understand the given inequality and what it represents. $\newline$ The inequality $0.9L + 0.3S \leq 6$ represents the maximum amount of pesto sauce Eldar can use to cook lasagna ( $L$ ) and spaghetti ( $S$ ). The coefficients $0.9$ and $0.3$ represent the amount of pesto sauce used per batch of lasagna and spaghetti, respectively.
Substitute spaghetti batches: Substitute the given number of spaghetti batches into the inequality. $\newline$ Eldar cooks $4$ batches of spaghetti, so we substitute $S = 4$ into the inequality: $\newline$ $0.9L + 0.3(4) \leq 6$
Simplify the inequality: Simplify the inequality by performing the multiplication. $0.9L + 1.2 \leq 6$
Isolate L: Isolate L by subtracting $1.2$ from both sides of the inequality. $\newline$ $0.9L \leq 6 - 1.2$
Find maximum pesto sauce for lasagna: Perform the subtraction to find the maximum amount of pesto sauce left for lasagna. $\newline$ $0.9L \leq 4.8$
Solve for L: Divide both sides of the inequality by $0.9$ to solve for $L$ . $\newline$ $L \leq \frac{4.8}{0.9}$
Find maximum lasagna batches: Perform the division to find the maximum number of lasagna batches Eldar can cook. $\newline$ $L \leq 5.333\ldots$ $\newline$ Since Eldar cannot cook a fraction of a batch, he can cook at most $5$ full batches of lasagna.