Solve The Problem??

Question

Dmitri needs 7 liters of a 29% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 35% solution and the other an unlimited supply of the 14% solution. How many liters of each solution should Dmitri use?

a. 35% solution: 2 liters; 14% solution: 15 liters
b. 35% solution: 5.5 liters; 14% solution: 1.5 liters
c. 35% solution: 4.5 liters; 14% solution: 2.5 liters
d. 35% solution: 5 liters; 14% solution: 2 liters

Answer 1

Answer a. is out immediately, because that adds up to 17 liters (unless it was a typo). Anyway...

Let A be the amount of the 35% solution (in liters)
Let B be the amount of the 14% solution (in liters)

Equation 1:
35% of A + 14% of B = 29% of (A + B)

You can drop the percent signs (multiply everything by 100)
35A + 14B = 29(A + B)

Equation 2:
A + B = 7

Now you have two equations and two unknowns:

Solve for B:
B = 7 - A

Substitute into the other equation:
35A + 14(7 - A) = 29(A + (7 - A))

Distribute the 14 and the 29 through the parentheses:
35A + 98 - 14A = 29(7)

Group 35A and -14A:
21A + 98 = 203

Subtract 98 from both sides:
21A = 203 - 98
21A = 105

Divide both sides by 21:
A = 105 / 21
A = 5

Solve for B:
B = 7 - A
B = 2

So the answer is:
D) 35% solution: 5 liters; 14% solution: 2 liters

Answer 2

x = amount of liters that has 35% solution of sulfuric acid
y = amount of litters that has 14% solution of sufuric acid

he needs 7 liters of both solutions, so:
x + y = 7

.35x is the amount of sulfuric acid in the solution that has 35% solution of sulfuric acid

.14y is the amount of sulfric in the solution that has 14% solution of sulfuric acid.

29% of that 7 liter will be the amount of acid, which are from both solution that has 35% solution of sulfurric acid and solution that has 14% solution of sulfurric acid

so
.35x + .14y = .29(7)
.35x + .14y = 2.03

x + y = 7
y = 7 - x

substitube

.35x + .14(7-x) = 2.03
.35x + .98 - .14x = 2.03
.21x = 1.05
x = 5

y = 7 - 5
y = 2

so the answer is D


Rec

Answer 3

let x lit of 35% and y lit of 14% sulfuric acid are mixed to get 7 lit of 29% sulfuric acid

since total is 7 liters

x + y = 7 ----------------------eqn(1)

x(35/100 ) + y(14/100) = 7(29/100)

35x + 14y = 203

divide by 7

5x + 2y = 29 ----------------eqn(2)

multiply eqn(1) with 2

2x + 2y = 14 -----------------eqn(3)

eqn(3) - eqn(2)

3x = 15

x = 15/3 = 5 lit

so y = 7-5 = 2 lit

so 5 lit of 35% and 2 lit of 14% should be mixed to get 7 lit of 29% solution