Math / Algebra

Question20. Нийло̄эр нь 134 -тэй т тнцуү гурван тооны I нь II-тайгаа $6: 7$ , II нь III-тай $3: 4$ харьцаа贝сгдыя бол ддгээр тоог ол.
27. Нийлбэр нь 156 -тай тэнцүү гурван тооны 1 нь II-тайгаа $3: 2$ , II нь III-тай $2: 7$ харьцаа

Studdy Solution

STEP 1

1. We have three numbers whose sum is 156.
2. The ratio of the first number to the second number is $3:2$ .
3. The ratio of the second number to the third number is $2:7$ .
4. We need to find the values of these three numbers.

STEP 2

1. Define variables for the three numbers based on the given ratios.
2. Express the relationships between the numbers using the ratios.
3. Write an equation for the sum of the numbers.
4. Solve the equation to find the values of the numbers.

STEP 3

Define variables for the three numbers. Let the first number be $3x$ , the second number be $2x$ , and the third number be $7y$ .

STEP 4

Express the relationships between the numbers using the ratios. From the given ratios, we have:
$\frac{3x}{2x} = \frac{3}{2}$ $\frac{2x}{7y} = \frac{2}{7}$
From the second ratio, solve for $x$ in terms of $y$ :
$2x = 7y \cdot \frac{2}{7}$ $x = y$

STEP 5

Write an equation for the sum of the numbers. Substitute $x = y$ into the expressions for the numbers:
First number: $3x = 3y$ Second number: $2x = 2y$ Third number: $7y$
The sum of the numbers is:
$3y + 2y + 7y = 156$

STEP 6

Simplify and solve the equation:
$12y = 156$
Divide both sides by 12 to solve for $y$ :
$y = \frac{156}{12}$ $y = 13$
Now substitute $y = 13$ back into the expressions for the numbers:
First number: $3y = 3 \times 13 = 39$ Second number: $2y = 2 \times 13 = 26$ Third number: $7y = 7 \times 13 = 91$
The three numbers are $39$ , $26$ , and $91$ .

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Studdy Solution

STEP 1

1. We have three numbers whose sum is 156.
2. The ratio of the first number to the second number is $3:2$ .
3. The ratio of the second number to the third number is $2:7$ .
4. We need to find the values of these three numbers.

STEP 2

1. Define variables for the three numbers based on the given ratios.
2. Express the relationships between the numbers using the ratios.
3. Write an equation for the sum of the numbers.
4. Solve the equation to find the values of the numbers.

STEP 3

Define variables for the three numbers. Let the first number be $3x$ , the second number be $2x$ , and the third number be $7y$ .

STEP 4

Express the relationships between the numbers using the ratios. From the given ratios, we have:
$\frac{3x}{2x} = \frac{3}{2}$ $\frac{2x}{7y} = \frac{2}{7}$
From the second ratio, solve for $x$ in terms of $y$ :
$2x = 7y \cdot \frac{2}{7}$ $x = y$

STEP 5

Write an equation for the sum of the numbers. Substitute $x = y$ into the expressions for the numbers:
First number: $3x = 3y$ Second number: $2x = 2y$ Third number: $7y$
The sum of the numbers is:
$3y + 2y + 7y = 156$

STEP 6

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Studdy Solution

STEP 1

1. We have three numbers whose sum is 156.2. The ratio of the first number to the second number is 3:23:23:2.3. The ratio of the second number to the third number is 2:72:72:7.4. We need to find the values of these three numbers.

STEP 2

1. Define variables for the three numbers based on the given ratios.2. Express the relationships between the numbers using the ratios.3. Write an equation for the sum of the numbers.4. Solve the equation to find the values of the numbers.

STEP 3

Define variables for the three numbers. Let the first number be 3x3x3x, the second number be 2x2x2x, and the third number be 7y7y7y.

STEP 4

STEP 5

Write an equation for the sum of the numbers. Substitute x=yx = yx=y into the expressions for the numbers:First number: 3x=3y3x = 3y3x=3y Second number: 2x=2y2x = 2y2x=2y Third number: 7y7y7yThe sum of the numbers is:3y+2y+7y=156 3y + 2y + 7y = 156 3y+2y+7y=156

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have three numbers whose sum is 156.
2. The ratio of the first number to the second number is $3:2$ .
3. The ratio of the second number to the third number is $2:7$ .
4. We need to find the values of these three numbers.

1. Define variables for the three numbers based on the given ratios.
2. Express the relationships between the numbers using the ratios.
3. Write an equation for the sum of the numbers.
4. Solve the equation to find the values of the numbers.

Define variables for the three numbers. Let the first number be $3x$ , the second number be $2x$ , and the third number be $7y$ .

Write an equation for the sum of the numbers. Substitute $x = y$ into the expressions for the numbers:
First number: $3x = 3y$ Second number: $2x = 2y$ Third number: $7y$
The sum of the numbers is:
$3y + 2y + 7y = 156$