Question

A/2=b/3=c/5, если a+b+c=30 ,найдите abc​

Answer 1

Ответ:

810

Объяснение:

если a=6, b=9, c=15

тогда 6/2=9/3=15/5

abc=6*9*15=810

Answer 2

To find the value of abc, we need to determine the values of a, b, and c. We can start by using the given ratios to relate the variables:

A/2 = b/3 = c/5

Let's choose a common factor for the ratios to simplify the equation. In this case, we can use 30 as the common factor since a + b + c = 30. Multiplying each ratio by 30, we get:

15A = 10b = 6c

Now, let's try to find the values of A, b, and c. Since these ratios are equal, we can equate any two expressions:

15A = 10b

Divide both sides by 5:

3A = 2b

Now, let's try to relate c to the values we found above. Since 6c = 10b, we can write:

c = (10b)/6

Now, we need to find the common factor between 10 and 6 to simplify the expression. The common factor is 2, so we get:

c = (5b)/3

Now, we know that a + b + c = 30, so we can substitute the values we found for b and c:

a + (3A)/2 + (5b)/3 = 30

Since 3A = 2b, we can replace A with (2b)/3:

a + (3A)/2 + (5b)/3 = a + (2b)/2 + (5b)/3 = a + b + (5b)/3 = 30

Now, we can isolate a:

a = 30 - b - (5b)/3

Now, we have expressions for a and c in terms of b. Let's find the value of b first:

a + b + c = 30

(30 - b - (5b)/3) + b + (5b)/3 = 30

30 - (5b)/3 + (5b)/3 = 30

30 = 30

This equation is always true, which means b can be any value. Let's choose a value for b to find the corresponding values for a and c. For simplicity, let's choose b = 6:

a = 30 - 6 - (5 * 6)/3

a = 30 - 6 - 10

a = 14

Now, let's find c:

c = (5 * 6)/3

c = 10

So, when b = 6, a = 14, and c = 10. Now, let's calculate the value of abc:

abc = 14 * 6 * 10

abc = 840

Therefore, when a + b + c = 30 and the given ratios hold true, the value of abc is 840.