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QuestionAn alloy is made by mixing 28g of 15% copper and 100g of 55% copper. Find the grams and percentage of copper in the mixture.

Studdy Solution

STEP 1

Assumptions1. The first alloy has a weight of28 grams and contains15% copper. . The second alloy has a weight of100 grams and contains55% copper.
3. The two alloys are mixed together completely, meaning the copper is evenly distributed in the resulting mixture.

STEP 2

First, we need to find the amount of copper in each alloy. We can do this by multiplying the weight of each alloy by the percentage of copper it contains.
For the first alloyCopper1=Weight1timesPercentage1Copper_{1} = Weight_{1} \\times Percentage_{1}For the second alloyCopper2=Weight2timesPercentage2Copper_{2} = Weight_{2} \\times Percentage_{2}

STEP 3

Now, plug in the given values for the weight and percentage of copper in each alloy to calculate the amount of copper.
For the first alloyCopper1=28 gramstimes15%Copper_{1} =28\, grams \\times15\%For the second alloyCopper2=100 gramstimes55%Copper_{2} =100\, grams \\times55\%

STEP 4

Convert the percentages to decimal values.
15%=0.1515\% =0.1555%=0.5555\% =0.55Then calculate the amount of copper in each alloy.
For the first alloyCopper1=28 gramstimes0.15Copper_{1} =28\, grams \\times0.15For the second alloyCopper2=100 gramstimes0.55Copper_{2} =100\, grams \\times0.55

STEP 5

Calculate the amount of copper in each alloy.
For the first alloyCopper1=28 gramstimes0.15=4.2 gramsCopper_{1} =28\, grams \\times0.15 =4.2\, gramsFor the second alloyCopper2=100 gramstimes0.55=55 gramsCopper_{2} =100\, grams \\times0.55 =55\, grams

STEP 6

Now that we have the amount of copper in each alloy, we can add these together to find the total amount of copper in the resulting mixture.
Total Copper=Copper1+Copper2Total\, Copper = Copper_{1} + Copper_{2}

STEP 7

Plug in the values for the amount of copper in each alloy to calculate the total amount of copper.
Total Copper=4.2 grams+55 gramsTotal\, Copper =4.2\, grams +55\, grams

STEP 8

Calculate the total amount of copper in the resulting mixture.
Total Copper=4.2 grams+55 grams=59.2 gramsTotal\, Copper =4.2\, grams +55\, grams =59.2\, grams

STEP 9

Now that we have the total amount of copper, we can find the percentage of copper in the resulting mixture by dividing the total amount of copper by the total weight of the mixture and then multiplying by100.
Percentage Copper=Total CopperTotal Weighttimes100%Percentage\, Copper = \frac{Total\, Copper}{Total\, Weight} \\times100\%

STEP 10

First, calculate the total weight of the mixture by adding the weights of the two alloys.
Total Weight=Weight+Weight2=28 grams+100 grams=128 gramsTotal\, Weight = Weight_{} + Weight_{2} =28\, grams +100\, grams =128\, grams

STEP 11

Now, plug in the values for the total amount of copper and the total weight of the mixture to calculate the percentage of copper.
Percentage Copper=59. grams128 gramstimes100%Percentage\, Copper = \frac{59.\, grams}{128\, grams} \\times100\%

STEP 12

Calculate the percentage of copper in the resulting mixture.
Percentage Copper=59.2 grams128 gramstimes100%=46.25%Percentage\, Copper = \frac{59.2\, grams}{128\, grams} \\times100\% =46.25\%(a) The resulting mixture contains59.2 grams of copper. (b) The percentage of copper in the resulting mixture is46.25%.

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