Question

2] The band has a ratio of boys to girls of 5 to 4. There are 52 girls in the band.

(Make sure to write out in words first.)
How many are boys?


How many total students?


I need work for both

Answer 1

Explanation:

For every 4 boys there are 5 girls and 9 students at the school. So that means that 49 of the students are boys. 49 of the total number of students is 120 students:

49×?=120

If 49 the number of students is 120, then 14 of 120 is 19 of the total number of students. In other words, 14×120=30 is 19 the total number of students. Then 9 times this amount will give the total number of students:

9×30=270

So there is a total of 270 students at the school. Note that this is equivalent to finding the answer to the division problem:

120÷49=?

We can see all of this very succinctly by using a tape diagram:

Bar_diagram_67722d3e6005449e4fbe5c57eaad4f3c

There are 4 units of boys and 9 units of students. Therefore 4/9 of the students are boys.

4 units = 120

1 unit = 30

9 units = 270

There are 270 students altogether.

Students can multiply the numbers in the first row by 10 to get the second row, and then double that amount to get the third row. Adding the entries in the second and third row gives the fourth row that has the solution.

Alternatively, since 120÷4=30, students can just multiply the numbers in the first row by 30 to get the values in the fourth row.

In every row, we can see that the fraction of the students that are boys is 49.

looking at the last row, we can see that the total number of students will be 4×30+5×30=120+150=270.