Question

Question #8fc9a

Answer 1

This is a straight proportion problem

Explanation:

Proportion problems are valuable when the rate of change is consistent. So, if 15 vials will treat 120 people, if the rate is consistent, that means that 30 vials would treat 240 people.

This is most often set up as rational proportion:

`\frac{15vials}{120p}=\frac{xvials}{1400p}`

Then, cross multiply:

`15*1400=120x`

21000=120x

x = `\frac{21000}{120}=175 vials`

Answer 2

`175`

Explanation:

`"using "color(blue)"proportion"`

`120" people "to15" vials"`

`1400to15/1xx1400/120=175" vials"`

Answer 3

You will need 175 vials for 1400 people

Explanation:

Let the unknown count of people be represented by `x`

`color(blue)("method 1")`

Using ratio but in fraction format.

`("vials")/("people")->15/120 -=x/1400`

Multiply by 1 and you do not change a value. However, 1 comes in many forms.

If we multiply `120` by `11 2/3` we get 1400

`("vials")/("people")->color(green)(15/120 color(red)(xx1) color(white)("d")->color(white)("d") 15/120 color(red)(xx(11 2/3)/(11 2/3)) =175/1400`

You will need 175 vials for 1400 people
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`color(blue)("Method 2")`

Determine how much of a vial you will need for one person. Then multiply that by the count of the people required

`("vials")/("120 people")-> ubrace(15/120 larr" vials per 120 people.")`
`color(white)("dddddddddddddddddddd.dd")uarr`
`color(white)("ddddddddddddddddddddd")"A ratio"`

`("part of a vial")/("1 person")-> (15-:120)/(120-:120) = ubrace(0.125/1larr" vials per person")`
`color(white)("dddddddddddddddddddddddddddddddddd")uarr`
`color(white)("ddddddddddddddddddddddddddddddd")"Still a ratio!"`

vials per 1400 people`->("vials")/("1400 person") =0.125xx1400=ubrace(175)`
`color(white)("dddddddddddddddddddddddddddddddddddddddddddd")uarr`
`color(white)("ddddddddddddd")` Only the top number of a fraction format ratio
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`color(blue)("Foot note")`

Although they may look different both methods are basically the same thing but presented in different ways.