Question

as part of a chemistry experiment, barry is making a mixture of two solutions. he uses 4 cups of solution a for every 2 cups of solution b. the table below shows the numbers of cups he uses of solution a and solution b. using the information from the table, choose the correct statement. a. the ratio of the number of cups of solution a to the total number of cups of the mixture is 3:2. b. the ratio of the number of cups of solution a to the total number of cups of the mixture is 2:3. c. there are 3 cups of solution a for every 6 cups of mixture.

Explanation:

Step1: Calculate the ratio of solution A to the total mixture

Take the first row: solution A is 4 cups, solution B is 2 cups. Total mixture is \(4 + 2=6\) cups. The ratio of solution A to total mixture is \(\frac{4}{4 + 2}=\frac{4}{6}=\frac{2}{3}\).

Step2: Check other rows for consistency

Second row: solution A = 8 cups, solution B = 4 cups. Total mixture \(8+4 = 12\) cups. Ratio of solution A to total mixture \(\frac{8}{8 + 4}=\frac{8}{12}=\frac{2}{3}\).
Third row: solution A = 12 cups, solution B = 6 cups. Total mixture \(12+6=18\) cups. Ratio \(\frac{12}{12 + 6}=\frac{12}{18}=\frac{2}{3}\).
Fourth row: solution A = 16 cups, solution B = 8 cups. Total mixture \(16 + 8=24\) cups. Ratio \(\frac{16}{16+8}=\frac{16}{24}=\frac{2}{3}\).

Answer:

B. The ratio of the number of cups of solution A to the total number of cups of the mixture is \(2:3\).