Answer :
"The correct answer C.17.1 oz of raisins are needed to make 3 lb of trail mix.
To solve this problem, we need to determine the proportion of raisins in the trail mix and then scale it up to the desired amount of trail mix.
First, we know that for every 1 lb of trail mix, 5.7 oz of raisins are required. We need to find out how many ounces of raisins are needed for 3 lb of trail mix.
Let's set up a proportion to find the amount of raisins needed for 3 lb of trail mix:
For 1 lb of trail mix, we need 5.7 oz of raisins. Therefore, for 3 lb of trail mix, we would need:
[tex]\[ \frac{5.7 \text{ oz of raisins}}{1 \text{ lb of trail mix}} = \frac{x \text{ oz of raisins}}{3 \text{ lb of trail mix}} \][/tex]
Now, we solve for x :
[tex]\[ x = \frac{5.7 \text{ oz} \times 3 \text{ lb}}{1 \text{ lb}} \] \[ x = 5.7 \text{ oz} \times 3 \] \[ x = 17.1 \text{ oz} \][/tex]
However, this calculation gives us the total amount of raisins needed for 3 lb of trail mix, not the additional amount needed beyond the initial 1 lb recipe. Since we already have 5.7 oz for the 1 lb recipe, we need to find out how much more we need for the additional 2 lb of trail mix
To find the additional amount of raisins needed for the extra 2 lb of trail mix, we subtract the amount already included in the 1 lb recipe from the total amount needed for 3 lb:
[tex]\[ \text{Additional raisins needed} = \text{Total raisins for 3 lb} - \text{Raisins for 1 lb} \] \[ \text{Additional raisins needed} = 17.1 \text{ oz} - 5.7 \text{ oz} \] \[ \text{Additional raisins needed} = 11.4 \text{ oz} \][/tex]
Since we are looking for the total amount of raisins needed to make 3 lb of trail mix from scratch, we should not subtract the initial 5.7 oz. The correct total amount of raisins needed for 3 lb of trail mix is 17.1 oz.
However, we must have made a mistake in our calculation because the options given are 1.9 oz, 8.7 oz, 17.1 oz, and 22.5 oz, and none of these match our incorrect total of 11.4 oz. Let's re-evaluate our calculation:
[tex]\[ x = 5.7 \text{ oz} \times 3 \] \[ x = 17.1 \text{ oz} \][/tex]
This is the correct calculation for the total amount of raisins needed for 3 lb of trail mix. The mistake was in thinking that we needed to calculate the additional amount of raisins. The question asks for the total amount needed to make 3 lb of trail mix, not the additional amount beyond 1 lb.
Therefore, the correct answer is 17.1 oz for the total amount of raisins needed for 3 lb of trail mix. However, this answer corresponds to option C, not D. It appears there was an error in the initial answer provided. The correct answer is indeed option C, 17.1 oz.
The final answer is:
[tex]\[ \boxed{17.1 \text{ oz}} \][/tex]
The answer is: 1[tex]7.1 \text{ oz}[/tex]."
Set up a proportion:
[tex]\frac{1}{5.7} = \frac{3}{x}[/tex]
The numerator represents the pounds of trail mix, and the denominator represents the ounces of raisins needed to create the pounds of trail mix.
Cross multiply the fractions:
[tex]1 \cdot x = 5.7 \cdot 3[/tex]
[tex]\boxed{x = 17.1}[/tex]
The answer will be C. 17.1 oz.
