A pharmacist wants to mix two solutions to obtain 100 cc of a solution that has an 8% concentration of a certain medicine. If one solution has a 10% concentration of the medicine and the second has a 5% concentration, how much od each of these solutions should she mix?
I am terrible with word problems and I just can't understand what's going on!? I don't know if this would help but we are currently on Linear Models, Equations and Inequalities, using substitution, elimination and graphical methods.
Thank you so much! My problem was that when I multiplied .08 by 100 I got 8 instead of the 800...so I wouldn't get the right answer...but I just went with it!(:
To solve this problem, we can use the concept of a mixture problem. Let's break down the information given to us:
Let's assume the pharmacist mixes x cc (cubic centimeters) of the 10% solution and (100 - x) cc of the 5% solution to obtain a total volume of 100 cc of an 8% solution.
Now, let's set up the equation based on the given information. The equation will express the total amount of medicine in the resulting mixture. Since we have two types of medicines:
Amount of medicine in the 10% solution + Amount of medicine in the 5% solution = Amount of medicine in the 8% solution
The amount of medicine in the 10% solution is 10% (concentration) multiplied by the volume of the 10% solution (x cc).
The amount of medicine in the 5% solution is 5% (concentration) multiplied by the volume of the 5% solution ((100 - x) cc).
Therefore, the equation is:
0.10x + 0.05(100 - x) = 0.08(100)
Now, let's solve this equation step-by-step:
Step 1: Distribute 0.05 to the terms inside the parentheses.
0.10x + 0.05 × 100 - 0.05x = 0.08 × 100
Step 2: Simplify the equation.
0.10x + 5 - 0.05x = 8
Step 3: Combine like terms on the left side.
0.05x + 5 = 8
Step 4: Subtract 5 from both sides.
0.05x = 8 - 5
0.05x = 3
Step 5: Divide both sides by 0.05.
x = 3 / 0.05
x = 60
The pharmacist should mix 60 cc of the 10% solution and (100 - 60) = 40 cc of the 5% solution to obtain 100 cc of a solution with an 8% concentration of the medicine.
I hope this step-by-step explanation helps! Let me know if you have any further questions.
No problem! Let's break down the problem step-by-step to understand what's happening.
The pharmacist wants to mix two solutions to obtain 100 cc of a solution that has an 8% concentration. This means she wants to find out how much of each solution she should mix to get the desired concentration.
Let's call the volume of the first solution she needs to mix as "x" cc, and the volume of the second solution as "y" cc. We need to find the values of x and y.
Next, let's consider the concentration of the first solution. It is given that it has a 10% concentration of the medicine. This means that in x cc of the first solution, 10% of it is the medicine. So, the amount of medicine in the first solution is 0.1x cc.
Similarly, for the second solution, it is given that it has a 5% concentration of the medicine. So, in y cc of the second solution, 5% of it is the medicine. Hence, the amount of medicine in the second solution is 0.05y cc.
Now, when we mix x cc of the first solution and y cc of the second solution, the total volume of the mixture is 100 cc. Therefore, we can write the equation:
x + y = 100 -- (Equation 1)
Additionally, we want the resulting solution to have an 8% concentration of the medicine. The total amount of medicine in the mixture is the sum of the amount of medicine in the first and second solutions, which is 0.1x + 0.05y cc. Remember that the total volume of the mixture is 100 cc. So the equation becomes:
(0.1x + 0.05y) / 100 = 0.08 -- (Equation 2)
Now we have two equations with two variables (x and y). We can solve this system of equations using the methods you mentioned: substitution, elimination, or graphical methods.
For example, we can solve it using substitution:
1. Solve Equation 1 for x:
x = 100 - y
2. Substitute the value of x in Equation 2:
(0.1(100 - y) + 0.05y) / 100 = 0.08
3. Simplify and solve for y:
(10 - 0.1y + 0.05y) / 100 = 0.08
(10 - 0.05y) / 100 = 0.08
10 - 0.05y = 0.08 * 100
10 - 0.05y = 8
-0.05y = 8 - 10
-0.05y = -2
y = -2 / -0.05
y = 40
4. Substitute the value of y back into Equation 1 to find x:
x + 40 = 100
x = 100 - 40
x = 60
So, the pharmacist needs to mix 60 cc of the first solution with 40 cc of the second solution to obtain 100 cc of a solution with an 8% concentration of the medicine.
I hope this explanation helps! If you have any further questions, feel free to ask.
So I will use two variables in the solution
let the amount of 10% solution used be x cc
let the amount of 5% solution be y cc
"A pharmacist wants to mix two solutions to obtain 100 cc" ---> x + y = 100
the new solution must contain 8% , so .08(100)
2nd equation:
.10x + .05y = .08(100)
I would multiply this by 100 to get rid of those nasty decimals
10x + 5y = 800
now divide by 5
2x + y = 160
so now we have
2x + y = 160
x + y = 100
subtract them:
x = 60
back in the first:
60+y = 100
y = 40
So they need 60 cc of the 10% solution and
40 cc of the 5% solution
check:
60+40 = 100, check!
.10(6) + .05(4) = .08(100
6+2 = 8 , check!