Question

select the table that represents the ratio of blue triangles to white triangles.

a.
blue 2 10 12 16
white 18 45 54 72

b.
blue 4 10 12 16
white 18 45 54 72

c.
blue 4 6 12 15
white 18 45 54 72

d.
blue 4 45 12 16
white 18 10 54 72

Explanation:

Step1: Count blue and white triangles

Count blue triangles: \(2\). Count white triangles: \(10\). Ratio is \(\frac{2}{10}=\frac{1}{5}\).

Step2: Check ratios in each table

• Table A:
• For \(2\) blue and \(18\) white: \(\frac{2}{18}=\frac{1}{9}

eq\frac{1}{5}\).

• Table B:
• For \(4\) blue and \(18\) white: \(\frac{4}{18}=\frac{2}{9}\).
• For \(10\) blue and \(45\) white: \(\frac{10}{45}=\frac{2}{9}\).
• For \(12\) blue and \(54\) white: \(\frac{12}{54}=\frac{2}{9}\).
• For \(16\) blue and \(72\) white: \(\frac{16}{72}=\frac{2}{9}\).
• Table C:
• For \(4\) blue and \(18\) white: \(\frac{4}{18}=\frac{2}{9}\).
• For \(6\) blue and \(45\) white: \(\frac{6}{45}=\frac{2}{15}

eq\frac{2}{9}\).

• Table D:
• For \(4\) blue and \(18\) white: \(\frac{4}{18}=\frac{2}{9}\).
• For \(45\) blue and \(10\) white: \(\frac{45}{10}=\frac{9}{2}

eq\frac{2}{9}\).

Wait, there is a mistake. Let's recount the original triangles. There are \(2\) blue and \(10\) white triangles. The ratio is \(\frac{2}{10}=\frac{1}{5}\). If we scale up: multiply numerator and denominator by \(2\), we get \(\frac{4}{20}\) (not in options). Multiply by \(5\), \(\frac{10}{50}\) (not in options). Wait, no, looking at the tables again, maybe the intended ratio is \(\frac{2}{10}=\frac{1}{5}\), and if we consider equivalent ratios. For table A: \(\frac{2}{18}=\frac{1}{9}\), \(\frac{10}{45}=\frac{2}{9}\), \(\frac{12}{54}=\frac{2}{9}\), \(\frac{16}{72}=\frac{2}{9}\). For table B: \(\frac{4}{18}=\frac{2}{9}\), \(\frac{10}{45}=\frac{2}{9}\), \(\frac{12}{54}=\frac{2}{9}\), \(\frac{16}{72}=\frac{2}{9}\). Wait, no, wait the original count: there are \(2\) blue and \(10\) white. If we consider that maybe the problem was mis - counted (maybe a typo in the problem's figure). If we assume the ratio of blue to white is \(2:10 = 1:5\). Let's check the tables for a constant ratio.

• Table A: \(\frac{2}{18}=\frac{1}{9}\), \(\frac{10}{45}=\frac{2}{9}\), not constant.
• Table B: \(\frac{4}{18}=\frac{2}{9}\), \(\frac{10}{45}=\frac{2}{9}\), \(\frac{12}{54}=\frac{2}{9}\), \(\frac{16}{72}=\frac{2}{9}\). The ratio of blue to white is \(\frac{2}{9}\) (if we consider \(4:18 = 2:9\), \(10:45=2:9\), \(12:54 = 2:9\), \(16:72=2:9\)).

Answer:

A.