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Vivek has a maximum of 49 seconds to chop tomatoes and zucchinis. It takes him 6 seconds to chop each tomato, and 4 seconds to chop each zucchini.
Write an inequality that represents the number of tomatoes
(T) and zucchinis
(Z) Vivek can chop within this time limit.

Vivek has a maximum of $49$ seconds to chop tomatoes and zucchinis. It takes him $6$ seconds to chop each tomato, and $4$ seconds to chop each zucchini. $\newline$ Write an inequality that represents the number of tomatoes $\newline$ $(T)$ and zucchinis $\newline$ $(Z)$ Vivek can chop within this time limit.

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Modeling with linear inequalities

Full solution

Q. Vivek has a maximum of

49

seconds to chop tomatoes and zucchinis. It takes him

6

seconds to chop each tomato, and

4

seconds to chop each zucchini.

\newline

Write an inequality that represents the number of tomatoes

\newline

(T)

and zucchinis

\newline

(Z)

Vivek can chop within this time limit.

Define Variables: Let's define the variables: $\newline$ $T =$ number of tomatoes Vivek can chop $\newline$ $Z =$ number of zucchinis Vivek can chop $\newline$ It takes $6$ seconds to chop each tomato and $4$ seconds to chop each zucchini. Vivek has a maximum of $49$ seconds to chop. $\newline$ The inequality will represent the total time spent chopping tomatoes and zucchinis, which cannot exceed $49$ seconds.
Write Inequality: Now, let's write the inequality based on the time it takes to chop each vegetable: $\newline$ $6 \text{ seconds/tomato} \times T \text{ tomatoes} + 4 \text{ seconds/zucchini} \times Z \text{ zucchinis} \leq 49 \text{ seconds}$ $\newline$ This translates to: $\newline$ $6T + 4Z \leq 49$
Check Inequality: We should check to make sure the inequality makes sense. If Vivek chops only tomatoes, he can chop at most $\frac{49}{6} \approx 8$ tomatoes (since he can't chop a fraction of a tomato, he can actually only chop $8$ tomatoes). If he chops only zucchinis, he can chop at most $\frac{49}{4} = 12$ zucchinis. The inequality $6T + 4Z \leq 49$ allows for combinations of $T$ and $Z$ that fit within the $49$ -second time limit.

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