Question

There are 1200 students at a school.

Each student has either a packed lunch or a school dinner.

62% of the students have school dinners.

55% of the students are girls.

45% of the girls have packed lunches.

How many boys have school dinners?

You must show all your working.

Answer 1

The number of boys that have school dinners is 381.

Explanation:

First, we need to find how many students have school dinners:

`SD = 1200*0.62 = 744`

The percent of girls that have school dinners:

`\%SD_(g) = 100\% - 45\% = 55\%`

Now, we need to find the number of boys (b) and girls (g) at a school:

`g = 1200*0.55 = 660`

`b=1200 - 660 = 540`

Hence. the percent of boys that have school dinners is given by:

`SD = g*\%SD_(g) + b*\%SD_(b)`

`\%SD_(b) = (SD - g*\%SD_(g))/(b) = (744 - 660*0.55)/(540) = 0.706`

`\%SD_(b) = 70.6\%`

Finally, the number of boys that have school dinners is:

`B = 540*0.706 = 381`

Therefore, the number of boys that have school dinners is 381.

I hope it helps you!