divide milk and coffee, each person gets the same amount of milk coffee but different proportions, one of them has 1/ 4 cups of coffee and 1/6 of milk, for a total of 8 oz. what is the total number of people?

Linear equation: an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution

Let,

The total amount of coffee= c

The total amount of milk = m

Total number of person = p

according to the question, c and m can't be .

Given,

Total amount of milk and coffee is 8 oz.

so,

[tex]\frac{c}{4} +\frac{m}{6} =8\\[/tex]

[tex]\frac{3c+2m}{12} =8[/tex]

So, this is linear equation.

3c+2m=8×12

[tex]$ \\$3 \mathrm{c}+2 \mathrm{~m}=96$[/tex]

and

[tex]\eq[/tex][tex]c+m=8p[/tex]

2(c+m) = 8p×2

[tex]2c+2m=24p[/tex] ...(2)

By equation 1 and 2

[tex]3c+2m=96\\ 2m=96-3c\\ 2c+2m=16p\\ 2c+96-3c=16p\\96-c=16p\\96=16p+c\\[/tex]

16p and 96 both are divisible by 16

So, let c =16k

Now 3c+2m =96

3(16k) +2m= 96

48k =2m= 96

k can't be 0, otherwise c is 0 and k cannot be 2, otherwise m is 0. Therefore k must be 1,

[tex]48+2m=96\\2m=96-48\\2m=48\\m=\frac{48}{2} \\m=24[/tex]

BY putting m=24 in equation (1)

[tex]3c+2m=96\\3c+2(24)=96\\3c+48=96\\3c=96-48\\3c=48\\c=\frac{48}{3} \\c=16[/tex]

Therefor, the number of person is 5

More information: brainly.in/question/25201905

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