College

Ms. Math's pasta sauce recipe uses 9 tomatoes for every 6 teaspoons of oil. Select all of the true statements:

- The recipe uses \(\frac{6}{9}\) teaspoons of oil per tomato.
- The recipe uses \(\frac{6}{9}\) tomatoes per teaspoon of oil.
- She needs 6 tomatoes for every 9 teaspoons of oil.
- She needs 2 teaspoons of oil for every 3 tomatoes.
- She needs 3 tomatoes for every 2 teaspoons of oil.

Answer :

Answer:

Options one and three

Step-by-step explanation:

Because the recipe uses 9 tomatoes for every 6 teaspoons of oil, we know that

[tex]9 t=6s[/tex]

where t is one tomato and s is one teaspoon of oil.

Therefore, we can use algebra to find that

[tex]t=\frac{6}{9}s[/tex]

and

[tex]s=\frac{9}{6}t[/tex]

meaning that for every tomato, 6/9 teaspoons of oil are used and for every teaspoon of oil, 9/6 tomatoes are used, so the first answer is correct and the second is not.

Next, we verify by plugging in the rest of the values.

For the third option, we check whether the following equation is true:

[tex]9*6=6*9[/tex]

Because the equation is true, we know that the statement is true.

Now, because options three and four mean the same thing, we can check both at the same time with equation

[tex]9*3=6*2[/tex]

Because this equation isn't true, we can conclude that neither option is true, leaving the answers to be options one and three.

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