Math / Algebra

Question41. $\frac{3 a+b}{2}=a+3 b$ бол $b$ нь $a$ -аас хэд дахин бага вэ?

Studdy Solution

STEP 1

1. The equation given is $\frac{3a + b}{2} = a + 3b$ .
2. We need to find how many times smaller $b$ is compared to $a$ .

STEP 2

1. Simplify the given equation.
2. Solve for $b$ in terms of $a$ .
3. Determine the ratio of $b$ to $a$ .

STEP 3

Start with the equation:
$\frac{3a + b}{2} = a + 3b$
Multiply both sides by 2 to eliminate the fraction:
$3a + b = 2(a + 3b)$

STEP 4

Distribute the 2 on the right side:
$3a + b = 2a + 6b$
Rearrange the equation to isolate terms involving $a$ and $b$ :
$3a + b - 2a - 6b = 0$
Simplify:
$a - 5b = 0$

STEP 5

Solve for $b$ in terms of $a$ :
$a = 5b$
$b = \frac{a}{5}$
This shows that $b$ is $\frac{1}{5}$ times $a$ .
The solution is that $b$ is $\frac{1}{5}$ times $a$ , meaning $b$ is 5 times smaller than $a$ .

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Question41. $\frac{3 a+b}{2}=a+3 b$ бол $b$ нь $a$ -аас хэд дахин бага вэ?

Studdy Solution

STEP 1

1. The equation given is $\frac{3a + b}{2} = a + 3b$ .
2. We need to find how many times smaller $b$ is compared to $a$ .

STEP 2

1. Simplify the given equation.
2. Solve for $b$ in terms of $a$ .
3. Determine the ratio of $b$ to $a$ .

STEP 3

Start with the equation:
$\frac{3a + b}{2} = a + 3b$
Multiply both sides by 2 to eliminate the fraction:
$3a + b = 2(a + 3b)$

STEP 4

Distribute the 2 on the right side:
$3a + b = 2a + 6b$
Rearrange the equation to isolate terms involving $a$ and $b$ :
$3a + b - 2a - 6b = 0$
Simplify:
$a - 5b = 0$

STEP 5

Solve for $b$ in terms of $a$ :
$a = 5b$
$b = \frac{a}{5}$
This shows that $b$ is $\frac{1}{5}$ times $a$ .
The solution is that $b$ is $\frac{1}{5}$ times $a$ , meaning $b$ is 5 times smaller than $a$ .

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Question41. 3a+b2=a+3b\frac{3 a+b}{2}=a+3 b23a+b​=a+3b бол bbb нь aaa-аас хэд дахин бага вэ?

Studdy Solution

STEP 1

1. The equation given is 3a+b2=a+3b \frac{3a + b}{2} = a + 3b 23a+b​=a+3b.2. We need to find how many times smaller b b b is compared to a a a.

STEP 2

1. Simplify the given equation.2. Solve for b b b in terms of a a a.3. Determine the ratio of b b b to a a a.

STEP 3

Start with the equation: 3a+b2=a+3b \frac{3a + b}{2} = a + 3b 23a+b​=a+3bMultiply both sides by 2 to eliminate the fraction:3a+b=2(a+3b) 3a + b = 2(a + 3b) 3a+b=2(a+3b)

STEP 4

Distribute the 2 on the right side:3a+b=2a+6b 3a + b = 2a + 6b 3a+b=2a+6bRearrange the equation to isolate terms involving a a a and b b b:3a+b−2a−6b=0 3a + b - 2a - 6b = 0 3a+b−2a−6b=0Simplify:a−5b=0 a - 5b = 0 a−5b=0

STEP 5

Solve for b b b in terms of a a a:a=5b a = 5b a=5bb=a5 b = \frac{a}{5} b=5a​This shows that b b b is 15\frac{1}{5}51​ times a a a. The solution is that b b b is 15\frac{1}{5}51​ times a a a, meaning b b b is 5 times smaller than a a a.

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Question41. $\frac{3 a+b}{2}=a+3 b$ бол $b$ нь $a$ -аас хэд дахин бага вэ?

1. The equation given is $\frac{3a + b}{2} = a + 3b$ .
2. We need to find how many times smaller $b$ is compared to $a$ .

1. Simplify the given equation.
2. Solve for $b$ in terms of $a$ .
3. Determine the ratio of $b$ to $a$ .

Start with the equation:
$\frac{3a + b}{2} = a + 3b$
Multiply both sides by 2 to eliminate the fraction:
$3a + b = 2(a + 3b)$

Distribute the 2 on the right side:
$3a + b = 2a + 6b$
Rearrange the equation to isolate terms involving $a$ and $b$ :
$3a + b - 2a - 6b = 0$
Simplify:
$a - 5b = 0$

Solve for $b$ in terms of $a$ :
$a = 5b$
$b = \frac{a}{5}$
This shows that $b$ is $\frac{1}{5}$ times $a$ .
The solution is that $b$ is $\frac{1}{5}$ times $a$ , meaning $b$ is 5 times smaller than $a$ .