There are 36 pupils in a class. Each girl is given 8 books and each boy is given 3 books. The total number of books the girls receive is 46 more than the total number of books the boys receive. How many girls are there in the class?

The ratio of the number of boys to that of girls in Class A is 2:3. The ratio of the number of girls who wear glasses to the number of girls who do not wear glasses is 1:3. If there are 12 more girls than boys, how many girls wear glasses?

The average height of 3 girls is 150cm. The heights of two of them are 1.6 m and 1.47 m. What is the height of the third girl?

A regular tank 40cm by 20cm by 20cm is filled with water up to 2/5 of its height. Water from a tap flows into the tank at 2.5 liters a minute. How much water is in the tank after 3 minutes? Give your answer in liters. (1Liter= 1000cm3)

GB = 8*G

BB = 3*B
GB - BB = 46

Where GB is the number of girl's books, BB is the number of boy's books, G is the number of girls, and B is the number of boys.

Use algebra to solve this system of equations

2nd problem

B/G = 2/3
G(glasses) + G(noglasses) = G
G(glasses)/G(noglasses) = 1/3
G - B = 12

where B is number of boys, G is number of girls, G(glasses) is number of girls with glasses, G(noglasses) is number of girls without glasses

Use algebra to solve this system of equations

3rd question:

1.6 m = 160 cm; 1.47 m = 147 cm

(160 + 147 + x) / 3 = 150

where x is the height of the third girl. Solve for x

4th question

The water in the tank before the tap turns on is

2/5 * 40 * 20 * 20 = 3200 cm3 = 3.2 L

After three minutes, 2.5 * 3 = 7.5 L

The total amount of water in the tank is 3.2 L + 7.5 L

1. number of girls ---- x

number of boys --- 36-x

8x - 3(36-x) = 46
8x - 108 + 3x = 46
11x = 154
x = 14

There are 14 girls in the class

2. number of boys = 2x
number of girls = 3x
1/4 of the girls wear glasses, or
(3/4)x girls wear glasses

"there are 12 more girls than boys" ---> x - (36-x) = 12
2x = 48
x = 24

There are 24 girls , and 1/4 of those wear glasses
Then 6 girls wear glasses

check:
24 girls and 12 boys, ratio is 12:24 = 2:3 , checks
1/4 of the 24 girls wear glasses ---> 6 girls wear glasses
ratio of glassed girl to non-glassed girls = 6 : 18 = 1:3 , checks
All is good!

3. (x+1.6+1.47)/3 = 1.50
x+1.6+1.47 = 4.5
x = 1.43

Third girl is 1.43 m or 143 cm tall

4. rate of flow = 2.5 L/min
after 3 minutes new amount of water = 3(2.5) = 7.5 L
plus the (2/5)(40)(20)(20) or 6400 mc^3 or 6.4 L already in tank
gives us 13.91 L

To find the number of girls in the class, we can set up the following equation:

8g = 3b + 46

Where g represents the number of girls and b represents the number of boys.

We also know that the ratio of boys to girls is 2:3, so we can set up a second equation:

b = (2/3)g - 12

Substituting this into the first equation, we get:

8g = 3((2/3)g - 12) + 46

Simplifying:

8g = 2g - 36 + 46
8g - 2g = 10
6g = 10
g = 10/6
g = 5/3

Since we can't have a fraction of a person, we'll round down to the nearest whole number. Therefore, there are 5 girls in the class.

To find the number of girls wearing glasses, we can use the information that the ratio of girls wearing glasses to those who do not wear glasses is 1:3.

Let's say the number of girls wearing glasses is x. Then the number of girls not wearing glasses would be 3x.

We also know that there are 12 more girls than boys, so:

x + 3x = 12

Combining like terms:

4x = 12

Dividing both sides by 4:

x = 12/4
x = 3

Therefore, there are 3 girls wearing glasses.

To find the height of the third girl, we can first find the average height of all three girls:

Average height = (1.6m + 1.47m + x)/3

We know that the average height is 150cm, so we can convert this to meters:

150cm = 1.5m

Setting up the equation and solving for x:

1.5 = (1.6 + 1.47 + x)/3

Multiplying both sides by 3:

4.5 = 1.6 + 1.47 + x

Simplifying:

4.5 = 3.07 + x

Subtracting 3.07 from both sides:

1.43 = x

Therefore, the height of the third girl is 1.43 meters.

To find the amount of water in the tank after 3 minutes, we first need to calculate the volume of the tank:

Volume of tank = Length x Width x Height
= 40cm x 20cm x 20cm
= 16,000cm³

Since we know that the tank is filled up to 2/5 of its height, we can calculate the filled volume:

Filled volume = (2/5) x 16,000cm³
= 6,400cm³

We also know that water flows into the tank at a rate of 2.5 liters per minute. Since 1 liter is equal to 1000cm³, the flow rate can be converted to cm³ per minute:

Flow rate = 2.5 liters/min x 1000cm³/liter
= 2500cm³/min

To find the amount of water in the tank after 3 minutes, we multiply the flow rate by the time:

Water in tank after 3 minutes = Flow rate x Time
= 2500cm³/min x 3 min
= 7500cm³

Finally, since 1 liter is equal to 1000cm³, we can convert the volume to liters:

Water in tank after 3 minutes = 7500cm³/1000
= 7.5 liters

Therefore, there are 7.5 liters of water in the tank after 3 minutes.

1. To solve this problem, we can set up a system of equations. Let's assume there are g girls and b boys in the class.

Given information:
Each girl is given 8 books, so the total number of books given to the girls is 8g.
Each boy is given 3 books, so the total number of books given to the boys is 3b.
The total number of books the girls receive is 46 more than the total number of books the boys receive, so we have the equation:

8g = 3b + 46 -----------(1)

We also know that there are 36 pupils in total, so we can set up another equation:

g + b = 36 -----------(2)

Now we have a system of equations with two variables (g and b). We can solve this system by substitution or elimination.

From equation (2), we can express b in terms of g:

b = 36 - g

Now substitute this expression for b in equation (1):

8g = 3(36 - g) + 46
8g = 108 - 3g + 46
8g + 3g = 108 + 46
11g = 154
g = 154/11
g = 14

Therefore, there are 14 girls in the class.

2. Let's assume there are g girls and b boys in Class A.

Given information:
The ratio of the number of boys to girls in Class A is 2:3, so we have:

b/g = 2/3 -----------(1)

The ratio of girls who wear glasses to those who do not wear glasses is 1:3. Let's denote the number of girls who wear glasses as x and the number of girls who do not wear glasses as y. We can write another equation:

x/y = 1/3 -----------(2)

We are also given that there are 12 more girls than boys, so we have:

g = b + 12 -----------(3)

Now let's solve this system of equations.

From equation (1), we can express b in terms of g:

b = (2/3)g

Substitute this expression for b in equation (3):

g = (2/3)g + 12
g - (2/3)g = 12
(1/3)g = 12
g = 12 * 3
g = 36

Substitute the value of g in equation (1) to find b:

b = (2/3) * 36
b = 24

Now we know there are 36 girls and 24 boys in Class A.

To find the number of girls who wear glasses, substitute the values of g and b in equation (2):

x/y = 1/3
x/(36 - x) = 1/3
3x = 36 - x
4x = 36
x = 36/4
x = 9

Therefore, there are 9 girls who wear glasses in Class A.

3. We are given the average height of 3 girls as 150cm, and the heights of two of them as 1.6m and 1.47m.

To find the height of the third girl, we need to find the sum of all three heights and subtract the sum of the known heights from it.

Let's calculate:

Total height = Average height * Number of girls
Total height = 150cm * 3
Total height = 450cm

Sum of known heights = 1.6m + 1.47m = 3.07m = 307cm

Height of the third girl = Total height - Sum of known heights
Height of the third girl = 450cm - 307cm
Height of the third girl = 143cm

Therefore, the height of the third girl is 143cm.

4. To find the amount of water in the tank after 3 minutes, we need to calculate the volume of water that flows into the tank during that time.

Given information:
The tank dimensions are 40cm by 20cm by 20cm.

First, calculate the volume of the tank:
Volume of the tank = Length * Width * Height
Volume of the tank = 40cm * 20cm * 20cm
Volume of the tank = 16000cm^3

The tank is filled up to 2/5 of its height, so the filled volume is:
Filled volume = (2/5) * 20cm
Filled volume = 8cm

Now calculate the volume of water that flows into the tank in 3 minutes:
Volume of water = Flow rate * Time
Volume of water = 2.5 liters/minute * 3 minutes
Volume of water = 7.5 liters

Convert the volume of water from liters to cm^3:
1 liter = 1000cm^3
7.5 liters = 7.5 * 1000cm^3
7.5 liters = 7500cm^3

Finally, calculate the total volume of water in the tank after 3 minutes:
Total volume of water = Filled volume + Volume of water
Total volume of water = 8cm + 7500cm^3
Total volume of water = 7508cm^3

Therefore, there are 7508cm^3 (or 7.508 liters) of water in the tank after 3 minutes.