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Answer :
Final answer:
The sets of ingredients in a proportional relationship with the original recipe are B, D, and E which are 6 Tbsp oil, 1.5 Tbsp vinegar, and 1 Tbsp honey; 18 Tbsp oil, 4.5 Tbsp vinegar, and 3 Tbsp honey; and 24 Tbsp oil, 6 Tbsp vinegar, and 4 Tbsp honey respectively.
Explanation:
The question is asking you to find which sets of measures maintain proportional relationships to the salad dressing recipe which uses 12 parts oil, 3 parts vinegar, and 2 parts honey. The easiest way to find out is to simplify the original ratio to its smallest components. In the original recipe, divide all parts by the smallest part, which is 2. This simplifies to a ratio of 6 oil: 1.5 vinegar: 1 honey.
Now you can compare this simplified ratio to each of the options.
A) 9 : 2 : 1.5 - is not proportional
B) 6 : 1.5 : 1 - is proportional
C) 15 : 4 : 3 - is not proportional
D) 18 : 4.5 : 3 - is proportional
E) 24 : 6 : 4 - is proportional
Therefore, sets B, D, and E are in a proportional relationship with the original recipe.
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The sets of ingredients are in a proportional relationship with the recipe is option (B) and (D).
- Proportions are commonly referred to as parts, portions, or numbers considered relative to the whole. The definition of ratio says that two ratios are proportional if they are equal.
- A ratio is a mathematical comparison of two numbers. If two groups of given numbers increase or decrease in the same proportion, the proportions are said to be directly proportional to each other. Ratios are indicated by the symbols '::' or '='.
It is given that salad dressing recipe uses 12 parts oil, 3 parts vinegar, and 2 parts honey.
(A) We will compare the quantity of given element to the option .
[tex]\frac{12}{9} =\frac{3}{2} =\frac{2}{1.5} \\\\\frac{4}{3} \neq \frac{3}{2} \neq \frac{4}{3}[/tex]
As the given quantities are not equal so , they are not proportional .
(B) We will compare the quantity of given element to the option .
[tex]\frac{12}{6} =\frac{3}{1.5} =\frac{2}{1} \\\\\frac{2}{1} = \frac{2}{1} =\frac{2}{1}[/tex]
As the given quantities are equal so , they are proportional .
(C) We will compare the quantity of given element to the option .
[tex]\frac{12}{15} =\frac{3}{4} =\frac{2}{3} \\\\\frac{4}{5} \neq \frac{3}{4} \neq \frac{2}{3}[/tex]
As the given quantities are not equal so , they are not proportional .
(D) We will compare the quantity of given element to the option .
[tex]\frac{12}{18} =\frac{3}{4.5} =\frac{2}{3} \\\\\frac{2}{3} = \frac{2}{3} = \frac{2}{3}[/tex]
As the given quantities are equal so , they are proportional .
(E) We will compare the quantity of given element to the option .
[tex]\frac{12}{24} =\frac{3}{2} =\frac{2}{4} \\\\\frac{1}{2} \neq \frac{3}{2} \neq \frac{1}{2}[/tex]
As the given quantities are not equal so , they are not proportional .
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