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Derin's boyfriend in Japan is $0.19 per minute. The rate to call her family in Turkey is
$0.12 per minute. Derin wants to spend at least
30 minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between
J, the number of minutes Derin calls Japan, and
T, the number of minutes Derin calls Turkey?
Choose 1 answer:
(A)
0.19 J+0.12 T <= 25

T <= 30
(B)
0.19 J+0.12 T >= 25

T <= 30
(C)
0.19 J+0.12 T <= 25

T >= 30
(D)
0.19 J+0.12 T >= 25
T >= 30

Derin's boyfriend in Japan is $\$0.19$ per minute. The rate to call her family in Turkey is $\$0.12$ per minute. Derin wants to spend at least $30$ minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between $J$ , the number of minutes Derin calls Japan, and $T$ , the number of minutes Derin calls Turkey? $\newline$ Choose $1$ answer: $\newline$ (A) $0.19J+0.12T \leq 25$ $\newline$ $T \leq 30$ $\newline$ (B) $0.19J+0.12T \geq 25$ $\newline$ $T \leq 30$ $\newline$ (C) $0.19J+0.12T \leq 25$ $\newline$ $T \geq 30$ $\newline$ (D) $0.19J+0.12T \geq 25$ $\newline$ $T \geq 30$

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Evaluate two-variable equations: word problems

Full solution

Q. Derin's boyfriend in Japan is

\$0.19

per minute. The rate to call her family in Turkey is

\$0.12

per minute. Derin wants to spend at least

30

minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between

J

, the number of minutes Derin calls Japan, and

T

, the number of minutes Derin calls Turkey?

\newline

Choose

1

answer:

\newline

(A)

0.19J+0.12T \leq 25

\newline

T \leq 30

\newline

(B)

0.19J+0.12T \geq 25

\newline

T \leq 30

\newline

(C)

0.19J+0.12T \leq 25

\newline

T \geq 30

\newline

(D)

0.19J+0.12T \geq 25

\newline

T \geq 30

Set Up Inequalities: We need to set up two inequalities: one to represent the cost of the calls and another to represent the time spent calling Turkey.
Total Cost Inequality: The first inequality will represent the total cost of the calls to Japan and Turkey. We don't know the exact amount Derin wants to spend, but we know it should be at least $\$25$ based on the options given. Therefore, the inequality will either be greater than or equal to $25$ ( $\geq 25$ ) or less than or equal to $25$ ( $\leq 25$ ).
Time Spent Inequality: The second inequality will represent the time Derin wants to spend calling Turkey. We know that Derin wants to spend at least $30$ minutes calling Turkey, so the inequality will be greater than or equal to $30$ ( $T \geq 30$ ).
Determine Cost Inequality: Now we need to determine whether the cost inequality should be greater than or equal to $25$ or less than or equal to $25$ . Since the problem states that Derin wants to spend ＂at least＂ $30$ minutes calling Turkey, it implies that she has a minimum budget she is willing to spend. Therefore, the cost inequality should be greater than or equal to $25$ ( $\geq 25$ ).
Combine Inequalities: Combining the two inequalities, we get the system: $\newline$ $0.19J + 0.12T \geq 25$ (for the cost) $\newline$ $T \geq 30$ (for the time calling Turkey)
Match Answer Choice: Looking at the answer choices, we see that option (D) matches our system of inequalities: $\newline$ (D) $0.19J + 0.12T \geq 25$ $\newline$ $T \geq 30$

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