SOLUTION: A shop that sells nuts has one mixture that is 30% pecans and 70% peanuts. A second mixture is 40% pecans and 60% peanuts. The manager wants to make a mixture that is 38% pecan

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Question 1069813: A shop that sells nuts has one mixture that is 30% pecans and
70% peanuts. A second mixture is 40% pecans and 60% peanuts.
The manager wants to make a mixture that is 38% pecans. She
wants to use 25 ounces more of the second mixture than the
first. How many ounces of each mixture should she use?
Thanks!
Found 3 solutions by Boreal, addingup, Edwin McCravy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
x of the first with .30pk+.70p
x+25 of the second with .40pk+.70p.
Total is 2x+25(.38)=.76x+9.50
.30x+.40(x+25)=.76x+9.50
.30x+.40x+10=.76x+9.50
0.5=0.06x
50=6x
x=8 1/3 oz of the first--.30(8.33)=2.50 oz pecans
x+25=33 1/3 oz of the second=.40(33 1/3)=13.33 oz pecans
That would be 41 2/3 oz with 15.83 oz pecans, and that is 38%.

Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website!
Let's call the weight of the first mixture x. Thus, the weight of the second mixture will be x+25, since you want to use 25oz. more of the second mixture than the first.
So, the total weight for our final mixture will be:
x+x+25 = 2x+25
:
Now for the weight of the pecans:
first mixture: 30% pecans = 0.3x.
second mixture:40% pecans = 0.4(x+25)
Lastly, we are looking for a mix with 38% pecans = 0.38(x+x+25)= 0.38(2x+25)
:
Put it all together:
0.3x+0.4(x+25) = 0.38(2x+25)
0.3x+0.4x+10 = 0.76x+9.5
0.7x = 0.76x-0.5 subtract 7x and add 0.5 to both sides
0.5 = 0.06x flip the equation, it looks better with the variable x on the left
0.06x = 0.5 divide both sides by 0.06
x = 8.33 So this is the weight of the first mixture. The second mixture, the problem says, will be 25 oz. more: 8.33+25 = 33.33oz.
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Additional info:
What will be the total weight of the final mixture? 8.33+33.33 = 41.66 ounces.
:
Happy learning,
John

Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!

The other tutors are correct, but I'll bet your teacher wants you to make a chart for mixture problems. So begin by making this chart: | ounces | percent | ounces of | |of nuts |(as decimal)| PECANS | ---------|--------|------------------------| 1st mix | | | | 2nd mix | | | | ---------|--------|------------|-----------| final mix| | | |

She wants to use 25 ounces more of the second mixture
than the first.

Let x = the number of ounces of the 1st mix. Then x+25 = the number of ounces of the 2nd mix. Fill those in | ounces | percent | ounces of | |of nuts |(as decimal)| PECANS | ---------|--------|------------------------| 1st mix | x | | | 2nd mix | x+25 | | | ---------|--------|------------|-----------| final mix| | | | Fill in the three percents expressed as decimals (hundredths) | ounces | percent | ounces of | |of nuts |(as decimal)| PECANS | ---------|--------|------------------------| 1st mix | x | 0.30 | | 2nd mix | x+25 | 0.40 | | ---------|--------|------------|-----------| final mix| | 0.38 | | Add the number of ounces of 1st and 2nd mixes to get the total number of ounces of final mix. x + x+25 = 2x+25. So fill that in for the ounces of final mix: | ounces | percent | ounces of | |of nuts |(as decimal)| PECANS | ---------|--------|------------------------| 1st mix | x | 0.30 | | 2nd mix | x+25 | 0.40 | | ---------|--------|------------|-----------| final mix| 2x+25 | 0.38 | | Next we fill in the last column with PECANs by taking the percentages of ounces of each of the three mixes. So we just multiply the two columns: | ounces | percent | ounces of | |of nuts |(as decimal)| PECANS | ---------|--------|------------------------| 1st mix | x | 0.30 |0.30x | 2nd mix | x+25 | 0.40 |0.40(x+25) | ---------|--------|------------|-----------| final mix| 2x+25 | 0.38 |0.38(2x+25)| The equation comes from adding up the ounces of PECANS in 1st and 2nd mixes and setting it equal the the number of ounces of PECANS in the final mix: 0.30x + 0.40(x+25) = 0.38(2x+25) Clear of decimals by moving them 2 places right: 30x + 40(x+25) = 38(2x+25) Solve that and get x = or Since we let x = the number of ounces of the 1st mix, the number of ounces of the 30% mixture is Since then x+25 = the number of ounces of the 2nd mix, the number of ounces of the 40% mixture is . Edwin