QuestionWhat percent of peanuts is in a mixture of $9 \mathrm{lbs}$ (55% peanuts) and $6 \mathrm{lbs}$ (40% peanuts)?

Studdy Solution

STEP 1

Assumptions1. The first mixture contains9 lbs of mixed nuts with55% peanuts. . The second mixture contains6 lbs of mixed nuts with40% peanuts.
3. We are mixing these two mixtures together.
4. We want to find the percentage of peanuts in the new mixture.

STEP 2

First, we need to find the total amount of peanuts in each mixture. We can do this by multiplying the total weight of each mixture by the percentage of peanuts in that mixture.
For the first mixture $eanuts_{1} = Weight_{1} \\times Percentage_{1}$ For the second mixture $eanuts_{2} = Weight_{2} \\times Percentage_{2}$

STEP 3

Now, plug in the given values for the weight and percentage of peanuts in the first mixture to calculate the amount of peanuts.
$eanuts_{1} =9\,lbs \\times55\%$

STEP 4

Convert the percentage to a decimal value.
$55\% =0.55$ $eanuts_{1} =9\,lbs \\times0.55$

STEP 5

Calculate the amount of peanuts in the first mixture.
$eanuts_{1} =9\,lbs \\times0.55 =4.95\,lbs$

STEP 6

Repeat the process for the second mixture. Plug in the given values for the weight and percentage of peanuts in the second mixture to calculate the amount of peanuts.
$eanuts_{2} =6\,lbs \\times40\%$

STEP 7

Convert the percentage to a decimal value.
$40\% =0.4$ $eanuts_{2} =6\,lbs \\times0.4$

STEP 8

Calculate the amount of peanuts in the second mixture.
$eanuts_{2} =6\,lbs \\times0.4 =2.4\,lbs$

STEP 9

Now that we have the amount of peanuts in each mixture, we can find the total amount of peanuts in the new mixture.
$Total\, peanuts = Peanuts_{} + Peanuts_{2}$

STEP 10

Plug in the values for the amount of peanuts in each mixture to calculate the total amount of peanuts.
$Total\, peanuts =4.95\,lbs +2.4\,lbs$

STEP 11

Calculate the total amount of peanuts in the new mixture.
$Total\, peanuts =4.95\,lbs +.4\,lbs =7.35\,lbs$

STEP 12

Now that we have the total amount of peanuts, we can find the total weight of the new mixture.
$Total\, weight = Weight_{} + Weight_{2}$

STEP 13

Plug in the values for the weight of each mixture to calculate the total weight.
$Total\, weight =9\,lbs +6\,lbs$

STEP 14

Calculate the total weight of the new mixture.
$Total\, weight =9\,lbs +6\,lbs =\,lbs$

STEP 15

Now that we have the total weight of the new mixture and the total amount of peanuts, we can find the percentage of peanuts in the new mixture.
$Percentage\, peanuts = \frac{Total\, peanuts}{Total\, weight}$

STEP 16

Plug in the values for the total amount of peanuts and the total weight to calculate the percentage of peanuts.
$Percentage\, peanuts = \frac{.35\,lbs}{15\,lbs}$

STEP 17

Calculate the percentage of peanuts in the new mixture.
$Percentage\, peanuts = \frac{7.35\,lbs}{15\,lbs} =0.49$

STEP 18

Convert the decimal value to a percentage.
$0.49 =49\%$ So,49% of the new mixture is peanuts.

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