Algebra, Choosing Integers in a Word Problem

[mapeslogan]

I have an issue with this problem, and I may be overthinking it. Here's the problem:

Choose three positive integers a, b, and c, so that c > b > a. Two liters of a c% acid solution needs to be diluted to a b% solution. How many liters of an a% acid solution should be mixed with the 2-liter solution?

I chose:

a=8
b=4
c=2

I then divided 2 liters by a which is (2) and got 1. 1 is how many goes into b (1 to 4). Multiply that by two and you get 2 liters to a which is 8. Correct me if I'm wrong. I have no idea where to start.

 

[Otis]

Choose three positive integers a, b, and c, so that c > b > a. Two liters of a c% acid solution needs to be diluted to a b% solution. How many liters of an a% acid solution should be mixed with the 2-liter solution?

I chose:

a=8
b=4
c=2

I then divided 2 liters by a which is (2) and got 1. 1 is how many goes into b (1 to 4). Multiply that by two and you get 2 liters to a which is 8. Correct me if I'm wrong. I have no idea where to start.

You need to assign values so that c > b > a.

You assigned values such that a > b > c, instead.

Also, pick a symbol to represent the unknown volume of the a% solution needed.

Then, try to do the following, and show us what you get.

Using your new value for c, calculate how much acid is in the two liters of c% solution.

Using your new value for a and also the symbol that you picked for the unknown volume of the a% solution, write an expression for the amount of acid in the a% solution.

The sum of those two acid amounts divided by the total volume of the mixture must be equal b%. This gives you an equation to solve, for the unknown amount of a% solution.

 

[mapeslogan]

You need to assign values so that c > b > a.

You assigned values such that a > b > c, instead.

Also, pick a symbol to represent the unknown volume of the a% solution needed.

Then, try to do the following, and show us what you get.

Using your new value for c, calculate how much acid is in the two liters of c% solution.

Using your new value for a and also the symbol that you picked for the unknown volume of the a% solution, write an expression for the amount of acid in the a% solution.

The sum of those two acid amounts divided by the total volume of the mixture must be equal b%. This gives you an equation to solve, for the unknown amount of a% solution.

x represents a%

so basically 2 liters of 8% needs to be diluted into 4%.

The equation I came up with was:

x=(4+4)/2 = 4

4+4 represents the amounts of solution for a and c which both summed and divided by 2 liters you get 4 liters which is b.

 

[mapeslogan]

x represents a%

so basically 2 liters of 8% needs to be diluted into 4%.

The equation I came up with was:

x=(4+4)/2 = 4

4+4 represents the amounts of solution for a and c which both summed and divided by 2 liters you get 4 liters which is b.

 

[Otis]

I got the same answer, but my equation is different.

I used the ratio of acid to total volume.

[2(0.08) + x(0.02)]/(x+2) = 4/100

:cool: