Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:

Amount of solution A to be used = A

Amount of solution B to be used = B

So, since we need to find two unknowns, we need to create a system of two equations to solve them.

Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:

A = 2 B

The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:

0.19 A + 0.14 B = 104

Now we can use our first equation to substitute A in terms of B in the second equation:

0.19 (2 B) + 0.14 B = 104

0.38 B + 0.14 B = 104

0.52 B = 104

B = 104 / 0.52

B = 200 milliliters

4 0

3 years ago

Factor –8x3 – 2x2 – 12x – 3 by grouping. what is the resulting expression? (2x2 – 3)(4x 1) (–2x2 – 3)(–4x 1) (2x2 – 3)(–4x 1) (–

myrzilka [38]

The factors of the expression are $\rm (4x+1)(-2x^2-3)$