ABC and def are parallel lines

A chemist has three different acid solutions,

serious [3.7K]

9514 1404 393

Answer:

36 liters of 20%
18 liters of 35%
54 liters of 55%

Step-by-step explanation:

Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...

a + b + c = 108 . . . . . total number of liters

.20a +.35b +.55c = 0.40·108 . . . . . liters of acid

0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution

__

Solving these three equations by your favorite method gives ...

(a, b, c) = (36, 18, 54)

The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.

_____

<em>Comment on alternate approach</em>

Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...

(3(.55) +1(.35))/4 = 0.50 = 50%

So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.

Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.

__

* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...

x(50%) +(1 -x)(20%) = 40%

x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x

x = (40% -20%)/(50% -20%)

The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.

3 0

4 years ago

3/4 divided by 9/13

kari74 [83]

Answer:

1.08

Step-by-step explanation:

to divide to fractions multiply one by the reciprocal of the other.

3/4 x 13/9 = 1.08

8 0

3 years ago

Read 2 more answers

1. __% of 4 is 7 <br><br> 2.__% of 75 is 25

jekas [21]

Answer:

1. 57.142857142857%

2. 33.33

7 0

3 years ago

In a random sample of 2500 sports fans, 61% prefer basketball over soccer.

timama [110]

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.

<h3>What is the margin of error?</h3>

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,

$MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%$