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?

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whitneytr12 whitneytr12 · Answer 1 · 2021-01-11T14:00:46+01:00

Answer:

The number of boys that have school dinners is 381.

Step-by-step explanation:

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

[tex] SD = 1200*0.62 = 744 [/tex]

The percent of girls that have school dinners:

[tex] \%SD_{g} = 100\% - 45\% = 55\% [/tex]

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

[tex] g = 1200*0.55 = 660 [/tex]

[tex]b=1200 - 660 = 540[/tex]

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

[tex] SD = g*\%SD_{g} + b*\%SD_{b} [/tex]

[tex]\%SD_{b} = \frac{SD - g*\%SD_{g}}{b} = \frac{744 - 660*0.55}{540} = 0.706[/tex]

[tex] \%SD_{b} = 70.6\% [/tex]

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

[tex]B = 540*0.706 = 381[/tex]

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

I hope it helps you!