A chemist is adding pure (100%) acid to a 12 liter solution that is 15% acid in order to increase it to 49% acid. How much pure acid must she add? How many ounces of 35% ethanol must be added to a 23 ounce mixture that contains 26% ethanol in order to obtain a mixture of 30.86% ethanol?

How many liters of 30% acid must be added to 10 liters of 53.66% acid in order to obtain a mixture that is 43% acid?

1) 8 liters of pure acid

2) 27 liters of 35% ethanol

3) 8.2 liters of 30% acid

Step-by-step explanation:

The inicial amount of acid is 15% of 12 L, and the inicial volume is 12L.

Adding 'x' L of 100% acid, we have the amount of acid equal to 12 * 0.15 + x * 1, and the volume of 12 + x. The concentration is the amount of acid over the volume, so we have that:

(12*0.15 + x) / (12 + x) = 49/100

(1.8 + x)*100 = (12 + x) * 49

180 + 100x = 588 + 49x

51x = 408

x = 8 liters of pure acid

Similar to the solution above, for the second question we have:

(23*0.26 + 0.35*x) / (23 + x) = 30.86/100

(5.98 + 0.35*x)*100 = (23 + x) * 30.86

598 + 35x = 709.78 + 30.86x

4.14x = 111.78

x = 27 liters of 35% ethanol

For the third question, we have:

(10*0.5366 + 0.3*x) / (10 + x) = 43/100

(5.366 + 0.3x)*100 = (10 + x)*43

536.6 + 30x = 430 + 43x

13x = 106.6

x = 8.2 liters of 30% acid

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

she will travel a distance in the range of 3 - 11 miles