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 $$ x $$.

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    and tests
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