QuestionFind the ratio $a : b$ for the equations: 19. $\frac{36}{b}=\frac{28}{a}$ and 20. $5a-3b=7b$ .

Studdy Solution

STEP 1

Assumptions1. $a$ and $b$ are non-zero numbers. We are asked to find the ratio $a b$
Problem19 $\frac{36}{b}=\frac{28}{a}$

STEP 2

First, we need to isolate $a$ in the equation. We can do this by cross multiplying.
$a = \frac{36 \times28}{b}$

STEP 3

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b = \frac{36 \times28}{b} b$

STEP 4

implify the ratio by cancelling out $b$ .
$a b =36 \times281$

STEP 5

Calculate the value of $36 \times28$ .
$a b =10081$ So, for problem19, the ratio $a b$ is $10081$ .
Problem20 $5a -3b =7b$

STEP 6

First, we need to isolate $a$ in the equation. We can do this by adding $3b$ to both sides of the equation and then dividing by5.
$a = \frac{5a}{5} = \frac{b +3b}{5}$

STEP 7

implify the equation to find the value of $a$ .
$a = \frac{10b}{5} =2b$

STEP 8

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b =2b b$

STEP 9

implify the ratio by cancelling out $b$ .
$a b =2$ So, for problem20, the ratio $a b$ is $2$ .

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QuestionFind the ratio $a : b$ for the equations: 19. $\frac{36}{b}=\frac{28}{a}$ and 20. $5a-3b=7b$ .

Studdy Solution

STEP 1

Assumptions1. $a$ and $b$ are non-zero numbers. We are asked to find the ratio $a b$
Problem19 $\frac{36}{b}=\frac{28}{a}$

STEP 2

First, we need to isolate $a$ in the equation. We can do this by cross multiplying.
$a = \frac{36 \times28}{b}$

STEP 3

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b = \frac{36 \times28}{b} b$

STEP 4

implify the ratio by cancelling out $b$ .
$a b =36 \times281$

STEP 5

Calculate the value of $36 \times28$ .
$a b =10081$ So, for problem19, the ratio $a b$ is $10081$ .
Problem20 $5a -3b =7b$

STEP 6

First, we need to isolate $a$ in the equation. We can do this by adding $3b$ to both sides of the equation and then dividing by5.
$a = \frac{5a}{5} = \frac{b +3b}{5}$

STEP 7

implify the equation to find the value of $a$ .
$a = \frac{10b}{5} =2b$

STEP 8

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b =2b b$

STEP 9

implify the ratio by cancelling out $b$ .
$a b =2$ So, for problem20, the ratio $a b$ is $2$ .

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QuestionFind the ratio a:ba : ba:b for the equations: 19. 36b=28a\frac{36}{b}=\frac{28}{a}b36​=a28​ and 20. 5a−3b=7b5a-3b=7b5a−3b=7b.

Studdy Solution

STEP 1

Assumptions1. aaa and bbb are non-zero numbers. We are asked to find the ratio aba babProblem19 36b=28a\frac{36}{b}=\frac{28}{a}b36​=a28​

STEP 2

First, we need to isolate aaa in the equation. We can do this by cross multiplying.a=36×28ba = \frac{36 \times28}{b}a=b36×28​

STEP 3

We are asked to find the ratio aba bab, so we can substitute the value of aaa from the equation above into the ratio.ab=36×28bba b = \frac{36 \times28}{b} bab=b36×28​b

STEP 4

implify the ratio by cancelling out bbb.ab=36×281a b =36 \times281ab=36×281

STEP 5

Calculate the value of 36×2836 \times2836×28.ab=10081a b =10081ab=10081So, for problem19, the ratio aba bab is 100811008110081.Problem20 5a−3b=7b5a -3b =7b5a−3b=7b

STEP 6

First, we need to isolate aaa in the equation. We can do this by adding 3b3b3b to both sides of the equation and then dividing by5.a=5a5=b+3b5a = \frac{5a}{5} = \frac{b +3b}{5}a=55a​=5b+3b​

STEP 7

implify the equation to find the value of aaa.a=10b5=2ba = \frac{10b}{5} =2ba=510b​=2b

STEP 8

We are asked to find the ratio aba bab, so we can substitute the value of aaa from the equation above into the ratio.ab=2bba b =2b bab=2bb

STEP 9

implify the ratio by cancelling out bbb.ab=2a b =2ab=2So, for problem20, the ratio aba bab is 222.

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QuestionFind the ratio $a : b$ for the equations: 19. $\frac{36}{b}=\frac{28}{a}$ and 20. $5a-3b=7b$ .

Assumptions1. $a$ and $b$ are non-zero numbers. We are asked to find the ratio $a b$
Problem19 $\frac{36}{b}=\frac{28}{a}$

First, we need to isolate $a$ in the equation. We can do this by cross multiplying.
$a = \frac{36 \times28}{b}$

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b = \frac{36 \times28}{b} b$

implify the ratio by cancelling out $b$ .
$a b =36 \times281$

Calculate the value of $36 \times28$ .
$a b =10081$ So, for problem19, the ratio $a b$ is $10081$ .
Problem20 $5a -3b =7b$

First, we need to isolate $a$ in the equation. We can do this by adding $3b$ to both sides of the equation and then dividing by5.
$a = \frac{5a}{5} = \frac{b +3b}{5}$

implify the equation to find the value of $a$ .
$a = \frac{10b}{5} =2b$

We are asked to find the ratio $a b$ , so we can substitute the value of $a$ from the equation above into the ratio.
$a b =2b b$

implify the ratio by cancelling out $b$ .
$a b =2$ So, for problem20, the ratio $a b$ is $2$ .