I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...
... 5x = 6(x -1.75)
(B) Subtract 5x, simplify and add the opposite of the constant.
... 5x -5x = 6x -6·1.75 -5x
... 0 = x -10.50
... 10.50 = x
(C) 5x = 5·10.50 = 52.50
... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value
(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.
Answer:
where are the multiple choice
Step-by-step explanation:
Hello!
Question 1
The angles in a triangle add up to 180°
Subtract the known angles from 180 to get x
180 - 105 - 40 = 35
The answer is 35
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Question 2
The angles in a triangle add up to 180°
The box means that angles is 90°
Subtract the know angles from 180 to get x
180 - 65 - 90 = 25
The answer is 25
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Hope this helps!
