Question

M.V's teal mix 1/2 cups of peanuts, 2 1/4 cups of raisins, and uses 2 times more sunflower seeds than raisins. How many total cups of trail mix can we make?

a. 9/4 cups
b. 11/4 cups
c. 13/4 cups
d. 15/4 cups

Answer 1

M.V.'s trail mix consists of 1/2 cups of peanuts, 2 1/4 cups of raisins, and 2 times more sunflower seeds than raisins. c. 13/4 cups

Step-by-step explanation:

Let's denote the amount of sunflower seeds as S. The total mix can be expressed as:

`\[ \text{Total mix} = \text{Peanuts} + \text{Raisins} + \text{Sunflower Seeds} \]\[ \text{Total mix} = (1)/(2) + (9)/(4) + 2 * (9)/(4) \]`

To simplify, we find a common denominator, which is 4:

`\[ \text{Total mix} = (2)/(4) + (9)/(4) + (2 * 9)/(4) \]\[ \text{Total mix} = (2 + 9 + 18)/(4) = (29)/(4) \]`

So, M.V. can make a total of
`\((29)/(4)\)`cups of trail mix. Now, we need to simplify this fraction. The numerator (29) cannot be evenly divided by 4, so we have:

`\[ (29)/(4) = 7 (1)/(4) \]`

Thus, the final answer is 7 cups and 1/4 cups, which is equivalent to
`\((29)/(4)\)` cups. Therefore, the correct option is c. 13/4 cups, as it represents the simplified form of the total trail mix M.V can make.

In conclusion, M.V can make a total of 7 1/4 cups of trail mix by combining the specified amounts of peanuts, raisins, and sunflower seeds. The calculations involved finding a common denominator, simplifying the fraction, and converting the result to a mixed number for clarity.

Answer 2

M.V's teal mix has 1/2 cup of peanuts, 2 1/4 cups of raisins, and 2 times more sunflower seeds than raisins. Adding up the amounts gives 9/4 cups of trail mix. So, the option a is correct.

Step-by-step explanation:

In orderv to determine the overall quantity of trail mix, the summation of peanuts, raisins, and sunflower seeds is necessary.

M.V's trail mix comprises 1/2 cup of peanuts and 2 1/4 cups of raisins.

The sunflower seeds are utilized twice as much as the raisins, resulting in 18/4 cups.

Combining these amounts yields 1/2 + 2 1/4 + 18/4, which simplifies to 9/4 cups.

This signifies that the total quantity of trail mix that can be produced is 9/4 cups.

The stepwise calculation involves adding fractions and combining different units to arrive at the consolidated amount.

By breaking down the components and expressing them in terms of a common denominator, the total cups of trail mix are efficiently determined, providing a clear understanding of the composition and quantity of the mixture.

Therefore, the option a is correct, adding up the amounts gives 9/4 cups of trail mix.