Math / Algebra

QuestionАав, ээж, хүү гурав өндрөө хэмжив. Ээжийн өндрийг $x$ гэвэл аав ээжээс 15 смээр өндөр, харин хүү эжээсээ 46 см-ээр намхан байсан бол аав, ээж, хүү гурвын өндрийн нийлбэрийг ол.

Studdy Solution

STEP 1

Assumptions
1. Let the height of the mother (ээж) be $x$ cm.
2. The father (аав) is 15 cm taller than the mother.
3. The son (хүү) is 46 cm shorter than the mother.
4. We need to find the sum of the heights of the father, mother, and son.

STEP 2

Express the height of the father in terms of $x$ .
The father's height is $x + 15$ cm.

STEP 3

Express the height of the son in terms of $x$ .
The son's height is $x - 46$ cm.

STEP 4

Write the expression for the sum of their heights.
The sum of the heights is:
$\text{Sum of heights} = \text{Mother's height} + \text{Father's height} + \text{Son's height}$

STEP 5

Substitute the expressions for each person's height into the sum.
$\text{Sum of heights} = x + (x + 15) + (x - 46)$

STEP 6

Simplify the expression by combining like terms.
$\text{Sum of heights} = x + x + 15 + x - 46$

STEP 7

Combine the $x$ terms and the constant terms.
$\text{Sum of heights} = 3x - 31$
The sum of the heights of the father, mother, and son is $3x - 31$ cm.

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Studdy Solution

STEP 1

Assumptions
1. Let the height of the mother (ээж) be $x$ cm.
2. The father (аав) is 15 cm taller than the mother.
3. The son (хүү) is 46 cm shorter than the mother.
4. We need to find the sum of the heights of the father, mother, and son.

STEP 2

Express the height of the father in terms of $x$ .
The father's height is $x + 15$ cm.

STEP 3

Express the height of the son in terms of $x$ .
The son's height is $x - 46$ cm.

STEP 4

Write the expression for the sum of their heights.
The sum of the heights is:
$\text{Sum of heights} = \text{Mother's height} + \text{Father's height} + \text{Son's height}$

STEP 5

Substitute the expressions for each person's height into the sum.
$\text{Sum of heights} = x + (x + 15) + (x - 46)$

STEP 6

Simplify the expression by combining like terms.
$\text{Sum of heights} = x + x + 15 + x - 46$

STEP 7

Combine the $x$ terms and the constant terms.
$\text{Sum of heights} = 3x - 31$
The sum of the heights of the father, mother, and son is $3x - 31$ cm.

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Studdy Solution

STEP 1

Assumptions1. Let the height of the mother (ээж) be xxx cm.2. The father (аав) is 15 cm taller than the mother.3. The son (хүү) is 46 cm shorter than the mother.4. We need to find the sum of the heights of the father, mother, and son.

STEP 2

Express the height of the father in terms of xxx.The father's height is x+15x + 15x+15 cm.

STEP 3

Express the height of the son in terms of xxx.The son's height is x−46x - 46x−46 cm.

STEP 4

Write the expression for the sum of their heights.The sum of the heights is:Sum of heights=Mother’s height+Father’s height+Son’s height\text{Sum of heights} = \text{Mother's height} + \text{Father's height} + \text{Son's height}Sum of heights=Mother’s height+Father’s height+Son’s height

STEP 5

Substitute the expressions for each person's height into the sum.Sum of heights=x+(x+15)+(x−46)\text{Sum of heights} = x + (x + 15) + (x - 46)Sum of heights=x+(x+15)+(x−46)

STEP 6

Simplify the expression by combining like terms.Sum of heights=x+x+15+x−46\text{Sum of heights} = x + x + 15 + x - 46Sum of heights=x+x+15+x−46

STEP 7

Combine the xxx terms and the constant terms.Sum of heights=3x−31\text{Sum of heights} = 3x - 31Sum of heights=3x−31The sum of the heights of the father, mother, and son is 3x−313x - 313x−31 cm.

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Assumptions
1. Let the height of the mother (ээж) be $x$ cm.
2. The father (аав) is 15 cm taller than the mother.
3. The son (хүү) is 46 cm shorter than the mother.
4. We need to find the sum of the heights of the father, mother, and son.

Express the height of the father in terms of $x$ .
The father's height is $x + 15$ cm.

Express the height of the son in terms of $x$ .
The son's height is $x - 46$ cm.

Write the expression for the sum of their heights.
The sum of the heights is:
$\text{Sum of heights} = \text{Mother's height} + \text{Father's height} + \text{Son's height}$

Substitute the expressions for each person's height into the sum.
$\text{Sum of heights} = x + (x + 15) + (x - 46)$

Simplify the expression by combining like terms.
$\text{Sum of heights} = x + x + 15 + x - 46$

Combine the $x$ terms and the constant terms.
$\text{Sum of heights} = 3x - 31$
The sum of the heights of the father, mother, and son is $3x - 31$ cm.