What is this I went brain dead i was so confused???

Question

Solution A is 25% acid and solution B is 40% acid. How much of each solution is needed to make 100 liters of 30% acid?

25L of A and 75L of B

66.7L of A and 33.3L of B

35.5L of A and 65L of B

34L of A and 66L of B

Solve for the variable.

|2x| = -5

-10/4

5

-5

no solution ( I think its this 1)

A grocer wishes to mix some peanuts worth $.90 per pound with some almonds worth $1.50 per pound. The grocer will make 150 pounds of a mixture that is worth $1.25 per pound. How much of each should she use?

50 pounds of peanuts and 80 pounds of almonds

55.5 pounds of peanuts and 62.5 pounds of almonds

60.7 pounds of peanuts and 91.5 pounds of almonds

62.5 pounds of peanuts and 87.5 pounds of almonds

The hypothesis of the proof below is:

If 3x - 1 = 11, then x = 4

x = 4

3x - 1 = 11

If 3x - 1 = 11, then x = 4

There is no hypothesis

Please work this problem out step by step

If 3x - 1 = 11, then x = 4

Answer 1

I'll give you two methods for the first one:

Method 1.  30% is 5% more than A and 10% more than B.  The difference between A and B is 15%, we want to bring the percentage up from A's percentage by 5 points, that's 1/3 of the total difference,  so we want 1/3 of the mixture to be B, the other 2/3 is to be A.

i.e. we want 100/3 L of B and 200/3 L of A.

Checking:  25% of 200/3 = 50/3

40% of 100/3 = 40/3

Total acid = 50/3 + 40/3 = 90/3 = 30L

which is indeed 30% of the 100L mixture.

Method 2.  If we take x L of A and (100-x) L  of B,

total acid = 0.25x + 0.4(100 - x)

This is to be 30 L, so we require

0.25x + 40 - 0.4x = 30

40 - 0.15x = 30

0.15x = 10

x = 10/0.15

.. = 200/3, multiplying top and bottom by 20.

100 - x = 100/3, which the second choice gives correct to one decimal place.

2. Yes, you're right, absolute value is non-negative, so

|2x| = -5 has no solutions.

3.  This is the same type as the first question.  Take x pounds of peanuts and 150 - x pounds of almonds, write the expression for their total value

0.9x + 1.5(150 - x) = 1.25*150

I'd multiply through by 20 here, to get rid of decimals

18x + 30(150 - x) = 3750

Hence12x = 750

and x = 750/12 = 125/2 = 62.5

150 - x = 87.5

confirming my intuition that the amount of peanuts is

35/60 of 150 pounds = 62.5 pounds.

4.  Basically a hypothesis is something starting with "if":

"If this, then that" -- the hypothesis is "this"

So in this question the hypothesis is

3x - 1 = 11.

If 3x - 1 = 11,

then 3x = 12 (adding 1 to both sides)

Then divide both sides by 3:

x = 4

Email me if there's anywhere I didn't give you enough detail.