Please help solve and explain this thank you
1 answer:
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Answer:
First brand of antifreeze: 21 gallons
Second brand of antifreeze: 9 gallons
Step-by-step explanation:
Let's call A the amount of first brand of antifreeze. 20% pure antifreeze
Let's call B the amount of second brand of antifreeze. 70% pure antifreeze
The resulting mixture should have 35% pure antifreeze, and 30 gallons.
Then we know that the total amount of mixture will be:
Then the total amount of pure antifreeze in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:
+
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We substitute the value of A into one of the two equations and solve for B.
Answer:
(x, y) = (40, 30)
Step-by-step explanation:
A graphing calculator can show you the solution to this system of equations is (x, y) = (40, 30). That is the point of intersection where the two lines cross.
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An algebraic solution can be found by using the substitution method. An expression for y can be found using the second equation:
y = 110 -2x . . . . . . subtract 2x from both sides
Using this in the first equation gives ...
3x -4(110 -2x) = 0 . . . . substitute for y
11x = 440 . . . . . . . . . simplify, add 440
x = 40 . . . . . . . . . . divide by 11
y = 110 -2(40) = 30
The solution is (x, y) = (40, 30).
