Question 1069813
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
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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)
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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.
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Happy learning,
John