Ascientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. to the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?

5.714 liters of the 5% solution and 4.286 of the 40%.

Step-by-step explanation:

Let x be the volume of 40% solution and y = volume of the 5% solution.

x + y = 10

0.40x + 0.05y = 0.20(x + y)

From the first equation x = 10 -y so we have:

0.40(10 - y) + 0.05y = 0.20( 10 - y + y)

4 - 0.40y + 0.05y = 2

-0.35y = -2

y = 5.714 liters of the 5%.

and x =  10 - 5.714 = 4.286  liters of the 40% solution.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300