The amounts of oil and vinegar combined to make the salad dressing are
in a constant definite proportion.
The quantity of oil required to make 28 teaspoons of dressing is 16
teaspoons.
Reasons:
According to the question, 4 parts of oil are added to every 3 parts of
vinegar.
Therefore;
The ratio or proportion of oil to vinegar in the salad dressing is 4 : 3
4 : 3 = [tex]\dfrac{4}{3}[/tex]
The proportion of oil to vinegar is therefore;
[tex]\mathrm{Amount \ of \ oil = \mathbf{\dfrac{4}{3} \times \ Amount \ of \ vinegar}}[/tex]
Which gives;
[tex]\mathrm{Amount \ of \ vinegar= \dfrac{3}{4} \times \ Amount \ of \ oil}[/tex]
Let x represent the amount of oil required to make 28 teaspoons of dressing,
we have;
[tex]\mathrm{Amount \ of \ vinegar \ required = \dfrac{3}{4} \times x}[/tex]
Which gives;
[tex]\mathrm{x + \dfrac{3}{4} \times x = 28}[/tex]
[tex]\mathrm{x + \dfrac{3}{4} \times x = \dfrac{7}{4} \times x = 28}[/tex]
Therefore;
[tex]x = \dfrac{4}{7} \times 28 = \dfrac{4}{7} \times 7 \times 4 = 4 \times 4 = 16[/tex]
The amount of oil required to make 28 teaspoons of dressing, x = 16 teaspoons.
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