It takes $250g$ of pasta and $240ml$ of sauce to make one batch of spaghetti, and it takes $600g$ of pasta and $700ml$ of sauce to make one batch of lasagna. Friedrich is a chef who wants to make spaghetti and lasagna using more than $4000g$ of pasta and more than $5000ml$ of sauce. Let $S$ denote the number of batches of spaghetti he makes and $L$ the number of batches of lasagna he makes. Write an inequality that represents the condition based on the number of grams of pasta. $\newline$ $250S + 600L > 4000$ $\newline$ Write an inequality that represents the condition based on the number of milliliters of sauce. $\newline$ $240S + 700L > 5000$

Full solution

Q. It takes

250g

of pasta and

240ml

of sauce to make one batch of spaghetti, and it takes

600g

of pasta and

700ml

of sauce to make one batch of lasagna. Friedrich is a chef who wants to make spaghetti and lasagna using more than

4000g

of pasta and more than

5000ml

of sauce. Let

S

denote the number of batches of spaghetti he makes and

L

the number of batches of lasagna he makes. Write an inequality that represents the condition based on the number of grams of pasta.

\newline

250S + 600L > 4000

\newline

Write an inequality that represents the condition based on the number of milliliters of sauce.

\newline

240S + 700L > 5000

Calculate Pasta Amounts: Calculate the total grams of pasta used for each batch of spaghetti and lasagna. For spaghetti, it's $250\text{g}$ per batch, and for lasagna, it's $600\text{g}$ per batch.
Set Pasta Inequality: Set up the inequality for the pasta condition. Friedrich wants to use more than $4000g$ of pasta. The inequality is $250S + 600L > 4000$ .
Calculate Sauce Amounts: Calculate the total milliliters of sauce used for each batch of spaghetti and lasagna. For spaghetti, it's $240\,\text{ml}$ per batch, and for lasagna, it's $700\,\text{ml}$ per batch.
Set Sauce Inequality: Set up the inequality for the sauce condition. Friedrich wants to use more than $5000\,\text{ml}$ of sauce. The inequality is $240S + 700L > 5000$ .