Question

modeling real life work with a partner. the soccer committee has 8 girls and 6 boys. the tennis committee has 9 girls and 8 boys. a friend tells you that the tennis committee has a greater portion of girls than the soccer committee. is your friend correct?

yes
no
explain. if not, how many boys could you add to the soccer committee so that your friend is correct?

Explanation:

Step1: Calculate the portion of girls in soccer committee

The soccer committee has \(8\) girls and \(6\) boys. The total number of members is \(8 + 6=14\). The portion of girls is \(\frac{8}{14}=\frac{4}{7}\approx0.571\).

Step2: Calculate the portion of girls in tennis committee

The tennis committee has \(9\) girls and \(8\) boys. The total number of members is \(9 + 8 = 17\). The portion of girls is \(\frac{9}{17}\approx0.529\).

Answer:

no. Since \(\frac{8}{14}\approx0.571\) (portion of girls in soccer committee) and \(\frac{9}{17}\approx0.529\) (portion of girls in tennis committee), \(0.571>0.529\). So the soccer committee has a greater portion of girls. To make the friend correct (tennis committee has a greater portion), let \(x\) be the number of boys added to soccer committee. Then \(\frac{8}{14 + x}<\frac{9}{17}\). Cross - multiply: \(8\times17<9\times(14 + x)\), \(136<126+9x\), \(9x>10\), \(x > \frac{10}{9}\approx1.11\). Since \(x\) is the number of boys (an integer), \(x = 2\) boys should be added.