In 2005, 24.8% of all Americans
were under 18 years old. Rhonda
conducts a survey of the ages of
students in eleventh grade at her school.
On November 1, she finds the average
age is 200 months. She also finds that
two-thirds of the students are within
6 months of the average age. Write and
solve an equation to determine the age
limits for this group of students. How
many months will it be until the first of
these students turn 18?

Question

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Respuesta :

rejkjavik rejkjavik · Answer 1 · 2018-10-14T22:17:08+02:00

Let's assume

x is the age of 11th grade student

we are given

Rhonda conducts a survey of the ages of students in eleventh grade at her school.

On November 1, she finds the average age is 200 months.

and

She also finds that two-thirds of the students are within 6 months of the average age.

so, we can set up equation as

[tex]|x-200|=3[/tex]

now, we can solve for x

[tex]x-200=3, x-200=-3[/tex]

[tex]x-200=3[/tex]

[tex]x-200+200=3+200[/tex]

[tex]x=203[/tex]

[tex]x-200=-3[/tex]

[tex]x-200+200=-3+200[/tex]

[tex]x=197[/tex]

So, the minimum age of 11th grade student is 197 months

So, the maximum age of 11th grade student is 203 months

now, we are given age is 18 years

we will change into months

[tex]18 years=12*18 months[/tex]

[tex]18 years=216 months[/tex]

So, first of these students turn 18 is

[tex]=216 -203[/tex]

[tex]=13[/tex] months...........Answer