# 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?

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 = 0Here,

- 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 = 32So, y = 3x i.e.

y = 3 * 32 = 96So, 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 = 14So, 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 = 8So, 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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