How much of a spice that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5%
salt?
2 answers:
<h3>Answer:</h3>
87.5 ounces
<h3>Explanation:</h3>There's a cute "X-diagram" tool that can be used for solving mixture problems of all kinds. (See the attachment.) The numbers on the left represent the percentages of the constituents of the mix. The number in the center is the desired percentage in the resultant mix. The numbers on the right in the X are the differences along the diagonals. (6-5=1, 5-3=2)
These are also the proportions of the constituents in the final mix. That is, there are 2 parts of spice that is 6% salt for each 1 part of spice that is 3% salt. So, we need half as much of the latter as the former.
Half of 175 ounces is 87.5 ounces, the amount of 3% spice that is needed.
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If you really want to write an equation, you can let x represent the amount of 3% spice needed. Then the amount of salt in the mix is ...
... 175×6% +x×3% = (175+x)×5%
Dropping the percent symbols and eliminating parentheses, we have
... 1050 +3x = 875 +5x
... (1050 -875) = (5x -3x) . . . . . add -875-2x
... 175/2 = x = 87.5 . . . . . . . . . . divide by the coefficient of x
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<u>ANSWER</u>
<u>EXPLANATION</u>
The given function is
We make the coefficient of unity by factoring
out of the last two terms to obtain;
We now add and subtract half the coefficient of multiplied by a factor of 6 to obtain;
We now factor 6 out of the last two terms to get;
The quadratic trinomial in the parenthesis is now a perfect square.
Hence the vertex form of the polynomial is