QuestionНамери стойността на $\frac{2 a+b+c}{a-2 b+2 c}$ , ако $a: b=5: 3$ и $b+c=a$ .

Studdy Solution

STEP 1

Assumptions1. The ratio $a b=53$ . The equation $b+c=a$
3. We need to find the value of the expression $\frac{ a+b+c}{a- b+ c}$

STEP 2

From the first assumption, we can express $a$ and $b$ in terms of a common variable $k$ . $a =5k$ $b =k$

STEP 3

Substitute the values of $a$ and $b$ in the equation $b+c=a$ to find the value of $c$ .
$3k + c =5k$

STEP 4

olve the equation for $c$ .
$c =k -3k =2k$

STEP 5

Now that we have the values of $a$ , $b$ , and $c$ , we can substitute these into the expression $\frac{2 a+b+c}{a-2 b+2 c}$ .
$\frac{2(5k) +3k +2k}{5k -2(3k) +2(2k)}$

STEP 6

implify the expression.
$\frac{10k +3k +2k}{5k -6k +4k}$

STEP 7

Further simplify the expression.
$\frac{15k}{3k}$

STEP 8

implify the expression to get the final answer.
$\frac{15k}{3k} =5$ So, the value of the expression $\frac{2 a+b+c}{a-2 b+2 c}$ is5.

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