Math / Algebra

QuestionA. $\frac{9}{11}$ B. $\frac{11}{9}$
9. $a: b: c: d=2: 3: 4: 7$ бол $\frac{2 a+3 b}{5 c-d}=$ ?

Studdy Solution

STEP 1

1. We are given a ratio $a: b: c: d = 2: 3: 4: 7$ .
2. We need to find the value of the expression $\frac{2a + 3b}{5c - d}$ .

STEP 2

1. Define variables based on the given ratio.
2. Substitute the variables into the expression.
3. Simplify the expression.

STEP 3

Define variables based on the given ratio. Assume a common multiple $k$ such that: $a = 2k, \, b = 3k, \, c = 4k, \, d = 7k$

STEP 4

Substitute the variables into the expression $\frac{2a + 3b}{5c - d}$ .
$\frac{2a + 3b}{5c - d} = \frac{2(2k) + 3(3k)}{5(4k) - 7k}$

STEP 5

Simplify the expression.
Calculate the numerator: $2(2k) + 3(3k) = 4k + 9k = 13k$
Calculate the denominator: $5(4k) - 7k = 20k - 7k = 13k$
Substitute back into the expression: $\frac{13k}{13k} = 1$
The value of the expression is:
$\boxed{1}$

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QuestionA. $\frac{9}{11}$ B. $\frac{11}{9}$
9. $a: b: c: d=2: 3: 4: 7$ бол $\frac{2 a+3 b}{5 c-d}=$ ?

Studdy Solution

STEP 1

1. We are given a ratio $a: b: c: d = 2: 3: 4: 7$ .
2. We need to find the value of the expression $\frac{2a + 3b}{5c - d}$ .

STEP 2

1. Define variables based on the given ratio.
2. Substitute the variables into the expression.
3. Simplify the expression.

STEP 3

Define variables based on the given ratio. Assume a common multiple $k$ such that: $a = 2k, \, b = 3k, \, c = 4k, \, d = 7k$

STEP 4

Substitute the variables into the expression $\frac{2a + 3b}{5c - d}$ .
$\frac{2a + 3b}{5c - d} = \frac{2(2k) + 3(3k)}{5(4k) - 7k}$

STEP 5

Simplify the expression.
Calculate the numerator: $2(2k) + 3(3k) = 4k + 9k = 13k$
Calculate the denominator: $5(4k) - 7k = 20k - 7k = 13k$
Substitute back into the expression: $\frac{13k}{13k} = 1$
The value of the expression is:
$\boxed{1}$

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QuestionA. 911\frac{9}{11}119​ B. 119\frac{11}{9}911​9. a:b:c:d=2:3:4:7a: b: c: d=2: 3: 4: 7a:b:c:d=2:3:4:7 бол 2a+3b5c−d=\frac{2 a+3 b}{5 c-d}=5c−d2a+3b​= ?

Studdy Solution

STEP 1

1. We are given a ratio a:b:c:d=2:3:4:7 a: b: c: d = 2: 3: 4: 7 a:b:c:d=2:3:4:7.2. We need to find the value of the expression 2a+3b5c−d \frac{2a + 3b}{5c - d} 5c−d2a+3b​.

STEP 2

1. Define variables based on the given ratio.2. Substitute the variables into the expression.3. Simplify the expression.

STEP 3

Define variables based on the given ratio. Assume a common multiple k k k such that: a=2k, b=3k, c=4k, d=7k a = 2k, \, b = 3k, \, c = 4k, \, d = 7k a=2k,b=3k,c=4k,d=7k

STEP 4

Substitute the variables into the expression 2a+3b5c−d \frac{2a + 3b}{5c - d} 5c−d2a+3b​.2a+3b5c−d=2(2k)+3(3k)5(4k)−7k \frac{2a + 3b}{5c - d} = \frac{2(2k) + 3(3k)}{5(4k) - 7k} 5c−d2a+3b​=5(4k)−7k2(2k)+3(3k)​

STEP 5

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QuestionA. $\frac{9}{11}$ B. $\frac{11}{9}$
9. $a: b: c: d=2: 3: 4: 7$ бол $\frac{2 a+3 b}{5 c-d}=$ ?

1. We are given a ratio $a: b: c: d = 2: 3: 4: 7$ .
2. We need to find the value of the expression $\frac{2a + 3b}{5c - d}$ .

1. Define variables based on the given ratio.
2. Substitute the variables into the expression.
3. Simplify the expression.

Define variables based on the given ratio. Assume a common multiple $k$ such that: $a = 2k, \, b = 3k, \, c = 4k, \, d = 7k$

Substitute the variables into the expression $\frac{2a + 3b}{5c - d}$ .
$\frac{2a + 3b}{5c - d} = \frac{2(2k) + 3(3k)}{5(4k) - 7k}$