After the addition of an acid, a solution has a volume of 90 milliliters. The volume of the solution is 3 milliliters greater th
1 answer:
Answer:
Step-by-step explanation:
Let be "x" the original volume of the solution (in milliliters) before the acid was added and "y" the volume of the solution (in milliliters) after the addition of the acid.
Set up a system of equations:
Applying the Substitution Method, you can substitute the second equation into the first equation and then solve for "x":
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<h3>Answer: 40</h3>
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Explanation:
The old dimensions of the rectangle were 30 by 15.
The new dimensions are 30+x by 15+x, where x is some positive number.
The new rectangle dimensions multiply to 1000
(30+x)(15+x) = 1000
Use the FOIL rule to expand out the left side like so
(30+x)(15+x) = 1000
450+30x+15x+x^2 = 1000
450+45x+x^2 = 1000
x^2+45x+450
Then lets get everything to one side
x^2+45x+450 = 1000
x^2+45x+450-1000 = 0
x^2+45x-550 = 0
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From here we use the quadratic formula
Plug in a = 1, b = 45, and c = -550.
Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.
The only practical answer is x = 10.
So each dimension is increased by 10 feet.
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If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25
Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.
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Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet