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Question

A graph with the x-axis representing oranges ranging from 0 to 36 in increments of 3 and the y-axis representing dollars ranging from 0 to 20 in increments of 1 shows six plotted points, 3 each for option A and option B. Option A has the following points: left parenthesis 12 comma 5 right parenthesis; left parenthesis 24 comma 10 right parenthesis; and left parenthesis 36 comma 15 right parenthesis. Option B has the following points: left parenthesis 9 comma 6 right parenthesis; left parenthesis 18 comma 12 right parenthesis; and left parenthesis 27 comma 18 right parenthesis.

Which coordinate pair should be plotted next for Option A to keep the ratio the same?

(1 point)
Responses

(48, 20)
left parenthesis 48 comma 20 right parenthesis

(37, 16)
left parenthesis 37 comma 16 right parenthesis

(40, 19)
left parenthesis 40 comma 19 right parenthesis

(41, 20)
left parenthesis 41 comma 20 right parenthesis
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Answer 1

To find the next coordinate pair for Option A that keeps the ratio the same, we first need to identify the current ratio of oranges to dollars for Option A.

The points for Option A are:

1. (12, 5) → ratio = 12/5 = 2.4
2. (24, 10) → ratio = 24/10 = 2.4
3. (36, 15) → ratio = 36/15 = 2.4

The ratio of oranges to dollars is consistently 2.4.

Now, let's denote the number of oranges by \( x \) and the number of dollars by \( y \). The ratio should stay the same, which means: \[ \frac{x}{y} = 2.4 \] From this, we can express \( y \) in terms of \( x \): \[ y = \frac{x}{2.4} \]

Let's examine the options given:

1. (48, 20): \[ \frac{48}{20} = 2.4 \quad \text{(This works)} \]

2. (37, 16): \[ \frac{37}{16} \approx 2.3125 \quad \text{(This does not work)} \]

3. (40, 19): \[ \frac{40}{19} \approx 2.1053 \quad \text{(This does not work)} \]

4. (41, 20): \[ \frac{41}{20} = 2.05 \quad \text{(This does not work)} \]

The only coordinate pair that keeps the ratio the same as 2.4 is: (48, 20)

Thus, the correct answer is: (48, 20).