Question

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?

Answer 1

`(51)/(46)`

Explanation:

Number of boys = B

Number of girls = G

Ratio of the number of boys to the number of girls in Ms. Zombo’s class =
`(3)/(4)`

`(B)/(G)=(3)/(4)\\\Rightarrow B=G(3)/(4)`

`B+G=49\\\Rightarrow G(3)/(4)+G=49\\\Rightarrow G(7)/(4)=49\\\Rightarrow G=28`

`B=G(3)/(4)\\\Rightarrow B=28(3)/(4)\\\Rightarrow B=21`

Ratio of the number of boys to the number of girls in Mr. Stolarski’s class =
`(5)/(3)`

`(B)/(G)=(5)/(3)\\\Rightarrow B=G(5)/(3)`

`B+G=48\\\Rightarrow G(5)/(3)+G=48\\\Rightarrow G(8)/(3)=49\\\Rightarrow G=18`

`B=G(8)/(3)\\\Rightarrow B=18(5)/(3)\\\Rightarrow B=30`

Total number of boys in combined class = 21+30 = 51

Total number of girls in combined class = 28+18 = 46

∴ Ratio of the number of boys to girls in the combined classes is
`\mathbf{(51)/(46)}`