1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paladinen [302]
3 years ago
7

The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

number of girls.​
Mathematics
1 answer:
mamaluj [8]3 years ago
5 0

Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:

\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are (15 + x) boys and girls in total. Using the formula for average:

\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

You might be interested in
Please Help Me With All Four ​
svetlana [45]

Answer:

answer below

Step-by-step explanation:

a is: 0.8

b is : 2

c is: 5

d is: 12.5

6 0
3 years ago
Read 2 more answers
What is 54 as a percentage of 216?<br> %
OlgaM077 [116]

Answer:

54 as a percentage of 216% is 116.64.

Step-by-step explanation:

100% of 54 is 54 so 54 x 2 would be 108. We have solved 200% of it now for the 16%. The percentage of 54 of 16% would be 8.64. Now add up all we have learned.

108 + 8.64 = 116.64

6 0
2 years ago
Can I please get help with this?
Andrei [34K]

Answer: x = 20.

Step-by-step explanation:

x and (3x + 10) combine to form a right angle, shown in the diagram by the small square joining the perpendicular lines.

Right angles are 90 degrees, so you can add both angles to get 90:

x + (3x + 10) = 90\\\\4x + 10 = 90\\\\4x = 80\\\\x = 20

7 0
3 years ago
A right triangle ABC is shown. Leg AC has length 18, leg BC has length 24, and hypotenuse AB has length 30. Find the exact value
Tresset [83]
Although there i no triangle given as the question requires, I am still going to answer because I understand it.

ABC is a right angled triangle. The triangle is 90° at C.

The trigonometric ratio sine is given by, sine = opposite/hypotenuse .
Cosine = adjacent/hypotenuse
 
So therefore, Sin A = 24/30
                               = 4/5

                     Cos A = 18/30
                               = 3/5
8 0
3 years ago
Read 2 more answers
The following polygons are similar. Find x
Ray Of Light [21]

is 750.000 is your answer.

5 0
2 years ago
Other questions:
  • Will give brainliest<br><br> What is the simplified form of 72x16/50x36 ? Assume x ≠ 0.
    12·2 answers
  • Each morning Rin rides 1.5 miles to school and then rides home in the afternoon. Later in the evening, she rides to the park and
    7·2 answers
  • What is the sum of ​ 4/15 + 8| 1/3 ​ ?
    5·1 answer
  • The table of values below shows data for a five-word spelling test. Number of Letters vs. Percentage who Spelled Correctly Word
    9·2 answers
  • A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.
    12·1 answer
  • Elisa buys a violin, which costs $2200, through a hire purchase agreement. Under the agreement, she
    10·1 answer
  • Help please :(..............
    9·2 answers
  • The FBI wants to determine the effectiveness of their 1010 Most Wanted list. To do so, they need to find out the fraction of peo
    12·1 answer
  • 5*23 <br> use the distubutive property and mental math to find the product
    11·1 answer
  • If we changed the 3 to a 0 in the equation, what would happen to the graph?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!