# What is the answer of 7y 4x

### Number puzzle 1

**Task:** The fivefold of a number reduced by $$ 6 $$ corresponds to double the number increased by $$ 9 $$. Calculate the number.

### (1) Determine what the variable stands for.

In the task you will find a hint on how to set the variable.

The task here is: Calculate the number.

#### $$ x: $$ the number you are looking for

### (2) Translate the text into the language of mathematics.

- five times a number: $$ 5x $$
- reduced by $$ 6 $$: $$ - 6 $$
- corresponds to: $$ = $$
- the double of a number: $$ 2x $$
- increased by $$ 9 $$: $$ + 9 $$

### (3) Write the equation.

The equation is: $$ 5x-6 = 2x + 9 $$

Now you have to solve the equation.

### Answer: The number you are looking for is $$ 5 $$.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

### Number puzzle 2

**Task:** The sum of three consecutive numbers is equal to four times the largest of the three numbers minus $$ 11 $$. Find the three numbers you are looking for.

### (1) Determine what the variable stands for.

In the task you will find a note on how to set the variable.

The task here is: Find the three numbers you are looking for.

The variable $$ x $$ can only refer to a number. Choose cleverly.

#### $$ x: $$ the smallest of the numbers searched for

### (2) Translate the text into the language of mathematics.

- the number following on $$ x $$: $$ x + 1 $$
- the number following on $$ x + 1 $$: $$ x + 2 $$
- Sum: addition ($$ + $$)
- four times the largest number: $$ 4 (x + 2) $$
- reduced by $$ 11 $$: $$ - 11 $$

### (3) Write the equation.

The equation is: $$ x + (x + 1) + (x + 2) = 4 (x + 2) -11 $$

Now you have to solve the equation.

### Answer: The numbers you are looking for are $$ 6,7,8 $$.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

### Age riddle

**Task:** Peter is three times as old as Beate. In four years they will be together $$ 16 $$ years old. How old are Beate and Peter today?

### (1) Determine what the variable stands for.

In the question you will find a hint on how to set the variable.

The question here is: How old are Beate and Peter today?

The variable $$ x $$ can only refer to either Beate's or Peter's age. Choose cleverly.

#### $$ x: $$ Beate's age

### (2) Translate the text into the language of mathematics.

- Today Peter is three times as old as Beate: $$ 3x $$
- Beates age in $$ 4 $$ years: $$ x + 4 $$
- Peter's age in $$ 4 $$ years: $$ 3x + 4 $$
- together: addition ($$ + $$)

### (3) Write the equation.

The equation is: $$ (x + 4) + (3x + 4) = 16 $$

Now you have to solve the equation.

### Answer: Beate is two years old today and Peter six years old.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

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### geometry

**Task:** The length of a rectangle is three times its width less five centimeters. The circumference of the rectangle is $$ 22 $$ $$ cm $$. Calculate the length and width of the rectangle.

### (1) Determine what the variable stands for.

In the task you will find a hint on how to set the variable.

The task here is: Calculate the length and width of the rectangle.

The variable $$ x $$ can only refer to either the length or the width. Choose cleverly.

#### $$ x: $$ Width of the rectangle

### (2) Translate the text into the language of mathematics.

- Triple width: $$ 3x $$
- reduced by $$ 5 $$ $$ cm $$: $$ - 5 $$
- Length of the rectangle: $$ 3x-5 $$
- Perimeter of the rectangle: length $$ + $$ width $$ + $$ length $$ + $$ width

### (3) Write the equation.

The equation is: $$ (3x-5) + x + (3x-5) + x = 22 $$

Now you have to solve the equation.

### Answer: The width of the rectangle is $$ 4 $$ cm and the length is $$ 7 $$ cm.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

### Everyday life 1

**Task:** A candle of $$ 20 $$ cm in size burns at $$ 15 $$ mm every hour. Another candle is $$ 25 $$ cm tall, but burns out at $$ 20 $$ mm every hour. After how many hours are the candles the same size?

### (1) Determine what the variable stands for.

In the task you will find a note on how to set the variable.

The question here is: after how many hours are the candles the same size?

You have to pay attention to the different units here.

### $$ x: $$ Candle burn time

### (2) Translate the text into the language of mathematics.

- Burning of $$ 15 $$ mm ($$ 1.5 $$ cm) per hour: $$ - 1.5x $$
- First candle after $$ x $$ hours: $$ 20-1.5x $$
- Burning of $$ 20 $$ mm ($$ 2 $$ cm) per hour: $$ - 2x $$
- Second candle after $$ x $$ hours: $$ 25-2x $$

### (3) Write the equation.

The equation is: $$ 20-1.5x = 25-2x $$

Now you have to solve the equation.

### Answer: After 10 hours the candles are the same size.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

### Everyday life 2

**Task:** You saved $$ 39 $$ € pocket money and today you spend everything on a total of eight comic books and CDs. How many comic books and how many CDs did you buy if each comic book cost $ 4.50 $ and each CD cost $ 5.50 $?

### (1) Determine what the variable stands for.

In the question or task you will find a hint on how to define the variable.

The question here is: How many comic books and how many CDs have you bought?

The variable $$ x $$ can only refer either to the number of comic books or the number of CDs.

#### $$ x: $$ number of CDs

### (2) Translate the text into the language of mathematics.

- Number of comic books: $$ 8-x $$
- Money invested in CDs: $$ 5.50x $$
- Money invested in comic books: $$ 4.50 (8-x) $$

### (3) Write the equation.

The equation is: $$ 5.50x + 4.50 (8-x) = 39 $$

Now you have to solve the equation.

### Answer: You bought five comic books and three CDs.

**(1)** First, determine what the variable stands for. **(2)** Translate the text into the language of math. **(3)** Write the equation.

Usually the variable is designated with $$ x $$.

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

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