Numbers - Quiz

Let's say that the number of boys is b and the number of girls is g. We know that the total number of boys and girls is 50, so we can write the equation:
b + g = 50

We also know that the total number of oranges that the boys receive is 5b, and the total number of oranges that the girls receive is 7g. The total number of oranges that are distributed is 280, so we can write the equation:
5b + 7g = 280

We can solve this system of equations using substitution. First, we can solve for b in the first equation by rearranging it as follows:
b = 50 - g

Substituting this expression for b into the second equation, we get:
5(50 - g) + 7g = 280

Expanding and simplifying the left side of the equation, we get:
250 - 5g + 7g = 280
Combining like terms, we get:
2g = 30
Dividing both sides by 2, we get:
g = 15
Therefore, there are 15 girls in the group of 50 people.

Let's say the number that the boy was supposed to multiply by 12 is x. We know that the boy multiplied this number by 21 instead, and got an answer that was 63 more than the correct answer. Therefore, we can write the equation:

12x + 63 = 21x
Subtracting 12x from both sides of the equation, we get:

63 = 9x
Dividing both sides of the equation by 9, we get:

7 = x
Therefore, the number that the boy was supposed to multiply by 12 is 7.

Let H be the number of hens and P be the number of pigs. The first equation is:

H + P = 84 (1)

The second equation is:

2H + 4P = 282 (2)

We can solve for P by dividing equation (2) by 2, which gives us:

H + 2P = 141 (3)

Subtracting equation (1) from equation (3) gives us:

H + 2P - H - P = 141 - 84

P = 57

Substituting this value for P into equation (1) gives us:

H + 57 = 84

H = 84 - 57

H = 27

Therefore, there are 27 hens in the poultry farm.

I hope this rephrased version makes the solution more clear. Let me know if you have any further questions.

We are given two numbers, A and B, such that A > B. The product of these numbers is 266 and the value of B is equal to 266 divided by A. We are also told that the difference between A and B is 5. Using this information, we can set up the following system of equations:

Equation 1: AB = 266
Equation 2: B = 266/A
Substituting Equation 2 into Equation 1, we get:

(266/A)A = 266

This simplifies to:

A^2 - 5A + 266 = 0

(A – 19)(A – 14) = 0
Therefore , A = 19 or A = 14
Hence, bigger number = A = 19

Let the incomes of P, Q, and R be 6x, 8x, and 11x, respectively, 
and their expenditures be 5y, 8y, and 12y, respectively. 
Therefore, 
their savings are (6x - 5y), (8x - 8y), and (11x - 12y), respectively.

If we set the ratio of x to y equal to 10/9, 
we can determine the ratio of the savings of P to Q and Q to R. 
The ratio of the savings of P to Q is 15/8, 
and the ratio of the savings of Q to R is 8/2.

The overall ratio of the savings of P, Q, and R is 15:8:2.

x = (2/5)x + 45
x = (3/5)x + 45
x = 75 

 To solve this problem, we can use the fact that the total number of 
marks a student receives is equal to the number of correct answers multiplied by 3, minus the
 number of wrong answers. We can represent this relationship with the equation:

3x - y = 38

Where x is the number of correct answers and y is the number of wrong answers.

We are also given that the total number of questions is 70, so we can set up
 a second equation to represent this relationship:

x + y = 70

We can solve this system of equations by first solving for y in the first equation:

y = 3x - 38

Substituting this expression for y into the second equation gives:

x + (3x - 38) = 70

This simplifies to:

4x - 38 = 70

Adding 38 to both sides gives:

4x = 108

Dividing both sides by 4 gives:

x = 27

Therefore, the student answered 27 questions correctly.   

In this case, let x and y be the two given numbers. We are given that the sum of x and y is 73 and that their difference is 28. We can express these two pieces of information as equations:
(x + y) = 73
(x - y) = 28
Using the difference of squares formula, we can now find the difference between the squares of x and y:
(x^2 - y^2) = (x + y)(x - y)
= 73 * 28
= 2044

Therefore, the difference between the squares of x and y is 2044

Given:

x + (15 - x) = 15
x^2 + (15 - x)^2 = 113
Find:

x and (15 - x)
Substitute the first equation into the expression for (15 - x) to get:

x^2 + (15 - x)^2 = 113
x^2 + 225 + x^2 - 30x + x^2 = 113
3x^2 - 30x + 112 = 0
Factor the quadratic equation:

(x - 7)(x - 8) = 0
Solve for x:

x = 7 or x = 8
Therefore, the two numbers are x = 7 and (15 - x) = 8.

To evaluate the expression "28% of 450 + 45% of 280", you can first find the value of 28% of 450 and 45% of 280.

To find 28% of 450, you can multiply 450 by 0.28, which is equal to 126.

To find 45% of 280, you can multiply 280 by 0.45, which is equal to 126.

Then, you can add these two values together to get the final result:
 126 + 126 = 252.

So, the expression "28% of 450 + 45% of 280" is equal to 252.