Joab set up camel and elephant rides for the Boerne Fall Festival. The ratio of camels to elephants was 2 to 3 and the maximum combined number of camels and elephants was was less than 20.

Question

Number of Camels,
Number of Elephants,
On the coordinate plane below, the -axis represents the number of camels and the -axis represents the number of elephants used to give rides at the Boerne Fall Festival.

Let be a possible number (camels, elephants) that Joab used to give rides at the Boerne Fall Festival based on the given ratio.

Two points are graphed that could represent the number of camels and elephants.

Use the table to help you find two more points that could represent the number of camels and elephants that Joab used, then graph the two points on the coordinate grid below.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -0.4 to 10.4 with ticks spaced every 1 unit(s).
The vertical axis goes from -0.4 to 10.4 with ticks spaced every 1 unit(s).
Point with coordinates (0, 0).
Point with coordinates (2, 3).
PointMove
UndoRedoReset
Animal Rides at Boerne Fall FestivalNumber of CamelsNumber of Elephants

Answer 1

To find additional points based on the ratio of camels to elephants (2 to 3) and the maximum combined number of animals (less than 20), we can start by establishing a few key details.

The ratio of camels (C) to elephants (E) is given as:

\[ \frac{C}{E} = \frac{2}{3} \]

This implies that:

\[ C = \frac{2}{3}E \]

or equivalently,

\[ E = \frac{3}{2}C \]

Since the total number of animals must be less than 20, we can set up the following equation:

\[ C + E < 20 \]

Substituting the equation of E from the ratio into the total:

\[ C + \frac{3}{2}C < 20 \]

Combining terms:

\[ \frac{5}{2}C < 20 \]

Multiplying both sides by 2 to eliminate the fraction:

\[ 5C < 40 \]

Dividing both sides by 5 gives:

\[ C < 8 \]

Since C must be a whole number and adhere to the ratio with E, we can select whole number values for C that are less than 8 that maintain the 2 to 3 relationship with E.

1. For \(C = 2\): \[ E = \frac{3}{2} \times 2 = 3 \] Point: (2, 3)

2. For \(C = 4\): \[ E = \frac{3}{2} \times 4 = 6 \] Point: (4, 6)

3. For \(C = 6\): \[ E = \frac{3}{2} \times 6 = 9 \] Point: (6, 9)

Now, let's gather the points based on the values we have calculated:

• Initial points are: (0, 0), (2, 3)
• New points are: (4, 6) and (6, 9)

The points (4, 6) and (6, 9) should be plotted on the coordinate plane where the x-axis represents the number of camels and the y-axis represents the number of elephants.

So the points to be plotted are:

• (4, 6)
• (6, 9)

Please plot these points accordingly on the graph.