Question

Натуральные числа а ,b и с таковы, что a:b=3:5 и b:с=4:7 . Чему равна дробь а+b/b+c ?

Answer 1

$a \div b = 3 \div 5 \\ a = \frac{3b}{5} \\ \\ b \div c = 4 \div 7 \\ c = \frac{7b}{4} \\ \\ \frac{a + b}{b + c} = \frac{ \frac{3b}{5} + b}{b + \frac{7b}{4} } = \frac{ \frac{3b}{5} + \frac{5b}{5} }{ \frac{4b}{4} + \frac{7b}{4} } = \frac{ \frac{8b}{5} }{ \frac{11b}{4} } = \frac{8b}{5} \times \frac{4}{11b} = \frac{32}{55}$

Answer 2

To solve this problem, let's first express the given ratios as equations and then find the values of 'a', 'b', and 'c'. Once we have the values, we can calculate the fraction 'a+b/b+c'.

Given: a:b = 3:5 and b:c = 4:7

Step 1: Express the ratios as equations: a/b = 3/5 ...(Equation 1) b/c = 4/7 ...(Equation 2)

Step 2: Find the values of 'a', 'b', and 'c': From Equation 1, we can express 'a' in terms of 'b': a = (3/5) * b

From Equation 2, we can express 'c' in terms of 'b': c = (7/4) * b

Step 3: Substitute the expressions for 'a' and 'c' in terms of 'b' into the fraction 'a+b/b+c': (a + b) / (b + c) = ((3/5) * b + b) / (b + (7/4) * b)

Step 4: Simplify the expression: (a + b) / (b + c) = (8/5 * b) / (15/4 * b)

Step 5: Cancel out 'b' from the numerator and denominator: (a + b) / (b + c) = (8/5) / (15/4)

Step 6: Now, to divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction: (a + b) / (b + c) = (8/5) * (4/15)

Step 7: Calculate the result: (a + b) / (b + c) = 32 / 75

So, the fraction a+b/b+c is equal to 32/75.