Math / Algebra

QuestionШилэн хоргонд туршилтын аалз, шоргоолжнууд байх ба аалз нь шоргоолжноос 50-аар цөөн юм. Аалз 8 хөлтэй, шоргоолж 6 хөлтэй ба харин нийт хөлийг нь тоолоход 1000 болж байв. Хэдэн аалз байсан бэ?

Studdy Solution

STEP 1

Assumptions
1. Let the number of spiders be $x$ .
2. The number of ants is $x + 50$ because there are 50 more ants than spiders.
3. Each spider has 8 legs.
4. Each ant has 6 legs.
5. The total number of legs is 1000.

STEP 2

Write an equation for the total number of legs. The total number of legs is the sum of the legs of the spiders and the ants.
$8x + 6(x + 50) = 1000$

STEP 3

Distribute the 6 in the equation.
$8x + 6x + 300 = 1000$

STEP 4

Combine like terms for $x$ .
$14x + 300 = 1000$

STEP 5

Subtract 300 from both sides to isolate the term with $x$ .
$14x = 700$

STEP 6

Divide both sides by 14 to solve for $x$ .
$x = \frac{700}{14}$

STEP 7

Calculate the value of $x$ .
$x = 50$
There were 50 spiders.

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Studdy Solution

STEP 1

Assumptions
1. Let the number of spiders be $x$ .
2. The number of ants is $x + 50$ because there are 50 more ants than spiders.
3. Each spider has 8 legs.
4. Each ant has 6 legs.
5. The total number of legs is 1000.

STEP 2

Write an equation for the total number of legs. The total number of legs is the sum of the legs of the spiders and the ants.
$8x + 6(x + 50) = 1000$

STEP 3

Distribute the 6 in the equation.
$8x + 6x + 300 = 1000$

STEP 4

Combine like terms for $x$ .
$14x + 300 = 1000$

STEP 5

Subtract 300 from both sides to isolate the term with $x$ .
$14x = 700$

STEP 6

Divide both sides by 14 to solve for $x$ .
$x = \frac{700}{14}$

STEP 7

Calculate the value of $x$ .
$x = 50$
There were 50 spiders.

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Studdy Solution

STEP 1

Assumptions1. Let the number of spiders be x x x.2. The number of ants is x+50 x + 50 x+50 because there are 50 more ants than spiders.3. Each spider has 8 legs.4. Each ant has 6 legs.5. The total number of legs is 1000.

STEP 2

Write an equation for the total number of legs. The total number of legs is the sum of the legs of the spiders and the ants.8x+6(x+50)=1000 8x + 6(x + 50) = 1000 8x+6(x+50)=1000

STEP 3

Distribute the 6 in the equation.8x+6x+300=1000 8x + 6x + 300 = 1000 8x+6x+300=1000

STEP 4

Combine like terms for x x x.14x+300=1000 14x + 300 = 1000 14x+300=1000

STEP 5

Subtract 300 from both sides to isolate the term with x x x.14x=700 14x = 700 14x=700

STEP 6

Divide both sides by 14 to solve for x x x.x=70014 x = \frac{700}{14} x=14700​

STEP 7

Calculate the value of x x x.x=50 x = 50 x=50There were 50 spiders.

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Assumptions
1. Let the number of spiders be $x$ .
2. The number of ants is $x + 50$ because there are 50 more ants than spiders.
3. Each spider has 8 legs.
4. Each ant has 6 legs.
5. The total number of legs is 1000.

Write an equation for the total number of legs. The total number of legs is the sum of the legs of the spiders and the ants.
$8x + 6(x + 50) = 1000$

Distribute the 6 in the equation.
$8x + 6x + 300 = 1000$

Combine like terms for $x$ .
$14x + 300 = 1000$

Subtract 300 from both sides to isolate the term with $x$ .
$14x = 700$

Divide both sides by 14 to solve for $x$ .
$x = \frac{700}{14}$

Calculate the value of $x$ .
$x = 50$
There were 50 spiders.