MATHEMATICS
COLLEGE

Answer:

Answer: 8.48528137...

or 6(square root 2)

or 6(square root 2)

MIDDLE SCHOOL

How many liters of a 10% saline solution must be added to to 4 liters of a 40% saline solution to obtain a 15% saline solution? A)20 L B)4 L C)2 L D)48 L Plz explain the steps and how to get answer

It would take 20 liters of the 10% solution.

We will let x be the amount of 10% solution in our problem. 10% saline in x liters is 0.1x. 4 liters of a 40% solution would be 4*0.4 = 1.6. We know that there are a total of x+4 liters in the final solution, and that it is 15% saline; that is 0.15(x+4). Our equation is then:

0.1x + 0.4(4) = 0.15(x+4)

0.1x+1.6 = 0.15*x + 0.15*4

0.1x+1.6 = 0.15x+0.6

We cannot have a variable on both sides; we will subtract 0.1x from both sides:

0.1x + 1.6 - 0.1x = 0.15x + 0.6 - 0.1x

1.6 = 0.05x + 0.6

Subtract 0.6 from both sides:

1.6 - 0.6 = 0.05x + 0.6 - 0.6

1 = 0.05x

Divide both sides by 0.05:

1/0.05 = 0.05x/0.05

20 = x

x was the 10% solution, so there are 20 liters of it.

We will let x be the amount of 10% solution in our problem. 10% saline in x liters is 0.1x. 4 liters of a 40% solution would be 4*0.4 = 1.6. We know that there are a total of x+4 liters in the final solution, and that it is 15% saline; that is 0.15(x+4). Our equation is then:

0.1x + 0.4(4) = 0.15(x+4)

0.1x+1.6 = 0.15*x + 0.15*4

0.1x+1.6 = 0.15x+0.6

We cannot have a variable on both sides; we will subtract 0.1x from both sides:

0.1x + 1.6 - 0.1x = 0.15x + 0.6 - 0.1x

1.6 = 0.05x + 0.6

Subtract 0.6 from both sides:

1.6 - 0.6 = 0.05x + 0.6 - 0.6

1 = 0.05x

Divide both sides by 0.05:

1/0.05 = 0.05x/0.05

20 = x

x was the 10% solution, so there are 20 liters of it.

MIDDLE SCHOOL

An electrician charges $30 for a service call, plus $75 per hour of service. If he charged $210, how many hours did he work?

Answer:

2.4 hours of service

Step-by-step explanation:

Set up an equation (h = hours):

30 + 75h = 210

Subtract 30 from each side:

75h = 180

Divide both sides by 75:

h = 2.4

HIGH SCHOOL

A jar has 15 marbles: 4 are green, 6 are red, and 5 are yellow. What is the probability that we will get a red marble or the green marble?

2/3

There are 4 green marbles and 6 red marbles, making 10 green or red marbles. The probability of drawing a red or a green marble is then 10/15 total marbles, which can be simplified to 2/3 by dividing the numerator and denominator each by 5.

COLLEGE

There are 1800 gym members in total. 3 4 are aged 25 - 59 years, 1 5 are over 60 years and the remainder are under 25 years. How many members are under 25 years?

There are 1751 members under the age of 25.