Open In App

Jane has 3 times as many cards as peter, the average number of cards owned by the two children is 64. How many cards does jane have?

Improve
Improve
Like Article
Like
Save
Share
Report

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the Number system. Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero.

An equation is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign. For example: In equation 3x+2 = 5, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign.

There are mainly 3 types of equations:

  • Linear Equation
  • Quadratic Equation
  • Polynomial Equation

Here, we will study the Linear equations.

Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x + 2 = 5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

  • 4x = 8
  • 5x + 10 = -20
  • 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

  • The numbers ‘a’ and ‘b’ are real.
  • Neither ‘a’ nor ‘b’ are equal to zero.

Solving Linear Equations in One Variable

The steps for solving an equation with only one variable are as follows:

Step 1: If there are any fractions, use LCM to remove them.

Step 2: Both sides of the equation should be simplified.

Step 3: Remove the variable from the equation.

Step 4: Make sure your response is correct.

Average of numbers: Average of  ‘N’ numbers is the total value/sum of N numbers divided by N i.e. 
Average of two numbers = (num1 + num2)/2
Average of three numbers = (num1 + num2 + num3)/2
and so on….

For example of Average of 4 and 6 will be (4 + 6)/2 = 10/2 i.e. 5

Example: Marks of the two students are 70 and 80 respectively. Find the average marks.

Solution: 

Average of two numbers are the sum of both numbers divided by 2.
So, here the average marks will be (70 + 80)/2 i..e 150/2 = 75

Jane has 3 times as many cards as peter, the average number of cards owned by the two children is 64. how many cards does Jane have?

Solution:

Let Peter have ‘x’  and Jane have ‘y’ number of cards respectively.

So, According to given statement
No. of cards Jane have = 3 * (No. of cards peter have )
i.e. y = 3x (Equation 1)

Also, it is given that average of both cards = 64 i.e.

(x + y)/2 = 64
Put the value of y = 3x from equation 1
(x + 3x) / 2 = 64
(4x) / 2 = 64
2x = 64
x = 64 / 2 
x = 32

So, y = 3x i.e. 
y = 3 * 32 = 96
So, the number of cards Peter and Jane have are 32 and 96 respectively.

Similar Questions

Question 1: A has 2 times as many coins as B, the average number of coins owned by both is 21. How many coins does A have?

Solution: 

Let A have ‘y’  and B have ‘x’ number of coins respectively.

So, According to given statement
No. of coins A have = 2 * (No. of coins B have)
i.e. y = 2x (Equation 1)

Also, it is given that average of both coins = 21 i.e.

(x + y) / 2 = 21
Put the value of y = 2x from equation 1
(x + 2x) / 2 = 21
(3x) / 2 = 21
3x = 42
x = 42 / 3
x = 14

So, y = 2x i.e. y = 2 * 14 = 28
So, the number of coins A and B have are 28 and 14 respectively.

Question 2: A has 5 times as many apples as B, the total number of apples owned by them both is 48. how many apples do both have?

Solution: 

Let A have ‘y’  and B have ‘x’ number of cards respectively.

So, According to given statement
No. of apples A have = 5 * (No. of apples B have )
i.e. y = 5x (Equation 1)

Also, it is given that total apples = 48 i.e.

(x + y)  = 48
Put the value of y = 5x from equation 1
(x + 5x) = 48
6x = 48
6x = 48
x = 48 / 6
x = 8

So, y = 5x i.e. y = 5 * 8 = 40
So, the number of apples A and B have are 40 and 8 respectively.


Last Updated : 02 Jan, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads