Q:

The ratio of the number of boys to the number of girls in Ms. Zombo’s class is 3 to 4. The ratio of the number of boys to the number of girls in Mr. Stolarski’s class is 5 to 3. If there are 49 students in Ms. Zombo’s class and 48 students in Mr. Stolarski’s class, what is the ratio of the number of boys to girls in the combined classes?

Accepted Solution

A:
Answer:[tex]\frac{51}{46}[/tex]Step-by-step explanation:Number of boys = BNumber of girls = GRatio of the number of boys to the number of girls in Ms. Zombo’s class = [tex]\frac{3}{4}[/tex][tex]\frac{B}{G}=\frac{3}{4}\\\Rightarrow B=G\frac{3}{4}[/tex][tex]B+G=49\\\Rightarrow G\frac{3}{4}+G=49\\\Rightarrow G\frac{7}{4}=49\\\Rightarrow G=28[/tex][tex]B=G\frac{3}{4}\\\Rightarrow B=28\frac{3}{4}\\\Rightarrow B=21[/tex]Ratio of the number of boys to the number of girls in Mr. Stolarski’s class = [tex]\frac{5}{3}[/tex][tex]\frac{B}{G}=\frac{5}{3}\\\Rightarrow B=G\frac{5}{3}[/tex][tex]B+G=48\\\Rightarrow G\frac{5}{3}+G=48\\\Rightarrow G\frac{8}{3}=49\\\Rightarrow G=18[/tex][tex]B=G\frac{8}{3}\\\Rightarrow B=18\frac{5}{3}\\\Rightarrow B=30[/tex]Total number of boys in combined class = 21+30 = 51Total number of girls in combined class = 28+18 = 46∴ Ratio of the number of boys to girls in the combined classes is [tex]\mathbf{\frac{51}{46}}[/tex]