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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?

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  • Last Updated : 17 Aug, 2021
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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.

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