math problem?

Question

vinegar solutions: white vinegar is a solution of acetic acid in water. there are two strengths of white vinegar----a 5% and a 10% solution. How many millilitres of each solution must be mixed to make 50 ml of a 9% vinegar solution?



i dont get this... so far i have "let x represent 5%solution" and "let y represent 10% solution" i have no clue what to do now?

Answer 1

Set up a simple set of equations such as
1. 0.09 * 50 = 0.05*x + 0.1*y
2. x + y = 50

Rearrange 2 to x = 50 - y and substitute into 1 to get:
0.09 * 50 = 0.05 * (50 - y) + 0.1*y
Multiplying out that gives:
4.5 = 2.5 - 0.05*y + 0.1*y
2 = 0.05*y
y = 40ml

Plug that value of y into equation 2 and find x.

Answer 2

ok, i learned how to solve these a different way . . .

first you set up what you're given:
5%(mL solution) + 10%(mL solution) = 9%(mL solution)

then you figure out variables for the "mL solution"
so, like you said let x=5% solution, and then since they give you the mL solution for the 9% (total mL = 50) and you're adding the amounts for 5% and 10%, then the total minus 5% has to equal the amount of 10%, in other words:

let x = mL of 5% solution
let 50 - x = mL of 10% solution

then, since we covered that the total has to be 50mL, you can set up your equation using the variables:

5%(x) + 10%(50 - x) = 9%(50)
change your percentages into decimals by moving the decimal 2 spaces to the left:

.05(x) + .1(50 - x) = .09(50)
then solve normally . . .
.05x + 5 - .1x = 4.5
(.05x - .1x ) +5 = 4.5
-.05x + 5 = 4.5
- 5 - 5
-.05x = -.5
divide by -.05 on both sides and get

x = 10mL

so you found how much 5% solution there is, now you have to find how much 10% solution there is by substituting 10 for x in your variable for the 10% solution (50 - x)
so:
50 - x
50 - 10
=40mL

so you need 10 mL of 5% solution and 40mL of 10% solution to make 50 mL of 9% solution.

lotsa luck

Answer 3

ok, so:
x = 5% solution
y = 10% solution

the amount of the mixture is 50ml
x + y = 50

.05x is the amount of the first vinegar solution
.10y is the amount of the seond vinegar solution

given that the mixture is 50 lm, and 9% are vinegar solution. So .09 * 50 = 4.5 ml is the amount of vinegar solution of the mixture

so .05x + .1y = 4.5

solve
x = 50 - y

.05 (50 - y) + .1y = 4.5
2.5 - .05y + .1y = 4.5
.05y = 2
y = 40ml

x = 50 - 40
x = 10 ml

so 10ml solution that has 5% vinegar solution
40ml solution that has 10% solution

hope it helps

Answer 4

Let 5%solution=x ml
& 10% solution=(50-x) ml
so x*5%+(50-x)*10%=50*9%
or 5x/100+(50-x)*10/100=50*9/100
or 5x+(50-x)10=450
or 5x+500-10x=450
or -5x=450-500
or -5x=-50
or x=10 so 50-x=40
so 5%=10 ml & 10%=40 ml ans

Answer 5

total =50 ml
x+y=50
vinegear needed =50*.09=4.5
.05x+.1y=4.5
x=50-y
.05(50-y)+.1y=4.5
2.5-.05y+.1y=4.5
.05y=2
y=40
x=10