Ratio Expression Value Problem
The problem asks us to find the value of the expression $\frac{5a - 3b}{7a + 2b}$ given that $a : b :: 3 : 4$.
Ratio Variable Setup
The given ratio $a : b :: 3 : 4$ means that $\frac{a}{b} = \frac{3}{4}$. We can express $a$ and $b$ in terms of a common factor, $k$.
- Let $a = 3k$
- Let $b = 4k$
Here, $k$ is a non-zero constant.
Expression Calculation Steps
Substitute these values ($a = 3k$, $b = 4k$) into the expression:
$ \frac{5a - 3b}{7a + 2b} = \frac{5(3k) - 3(4k)}{7(3k) + 2(4k)} $
Simplify the numerator and the denominator separately:
- Numerator: $5(3k) - 3(4k) = 15k - 12k = 3k$
- Denominator: $7(3k) + 2(4k) = 21k + 8k = 29k$
The expression now becomes:
$ \frac{3k}{29k} $
Value Simplification Result
Since $k \neq 0$, we can cancel $k$ from the numerator and the denominator.
$ \frac{3k}{29k} = \frac{3}{29} $
Thus, the value of the expression is $\frac{3}{29}$.
Similar Questions
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
