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Ezra enjoys gardening.
Let
S represent the number of sunflower plants and
L represent the number of lily plants Ezra's water supply can water.

0.7 S+0.5 L <= 11
Ezra waters 10 lily plants. How many sunflower plants can he water at most with the remaining amount of water?
Choose 1 answer:
(A) Ezra can water 7 sunflower plants at most.
(B) Ezra can water 8 sunflower plants at most.
(C) Ezra can water 10 sunflower plants at most.
(D) Ezra can water 11 sunflower plants at most.

Ezra enjoys gardening. $\newline$ Let $S$ represent the number of sunflower plants and $L$ represent the number of lily plants Ezra's water supply can water. $\newline$ $0.7S + 0.5L \leq 11$ $\newline$ Ezra waters $10$ lily plants. How many sunflower plants can he water at most with the remaining amount of water? $\newline$ Choose $1$ answer: $\newline$ (A) Ezra can water $7$ sunflower plants at most. $\newline$ (B) Ezra can water $8$ sunflower plants at most. $\newline$ (C) Ezra can water $10$ sunflower plants at most. $\newline$ (D) Ezra can water $11$ sunflower plants at most.

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Modeling with linear inequalities

Full solution

Q. Ezra enjoys gardening.

\newline

Let

S

represent the number of sunflower plants and

L

represent the number of lily plants Ezra's water supply can water.

\newline

0.7S + 0.5L \leq 11

\newline

Ezra waters

10

lily plants. How many sunflower plants can he water at most with the remaining amount of water?

\newline

Choose

1

answer:

\newline

(A) Ezra can water

7

sunflower plants at most.

\newline

(B) Ezra can water

8

sunflower plants at most.

\newline

(C) Ezra can water

10

sunflower plants at most.

\newline

(D) Ezra can water

11

sunflower plants at most.

Substitute lily plants: Substitute the number of lily plants $L$ into the inequality. $\newline$ Given that Ezra waters $10$ lily plants, we substitute $L = 10$ into the inequality $0.7S + 0.5L \leq 11$ . $\newline$ $0.7S + 0.5(10) \leq 11$
Perform multiplication: Perform the multiplication to simplify the inequality. $0.7S + 5 \leq 11$
Isolate S: Isolate S by subtracting $5$ from both sides of the inequality. $\newline$ $0.7S \leq 11 - 5$ $\newline$ $0.7S \leq 6$
Divide by $0$ . $7$ : Divide both sides of the inequality by $0.7$ to solve for $S$ . $\newline$ $S \leq \frac{6}{0.7}$
Find maximum number of sunflower plants: Perform the division to find the maximum number of sunflower plants Ezra can water. $\newline$ $S \leq 8.57142857\ldots$ $\newline$ Since Ezra cannot water a fraction of a plant, we round down to the nearest whole number. $\newline$ $S \leq 8$

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