1f a:b = 6:5, Find the value of
(4a + 6b/3a − b) ÷ (4a/5b)
A. -73
B. 73
C. -7.03
D. 7.03
To find the value of the expression, let's substitute a and b with their respective values in terms of each other.
Since a:b = 6:5, we can set up the equation 6x = 5y, where x = a and y = b.
From this equation, we can solve for a in terms of b:
a = 5y/6
Now, let's substitute these values into the expression:
(4a + 6b/3a − b) ÷ (4a/5b)
= (4(5y/6) + 6b)/(3(5y/6) − b) ÷ (4(5y/6)/(5b))
= (20y/6 + 6b)/(15y/6 − b) ÷ (20y/6)/(5b)
= (20y + 6b)/(15y − 6b) ÷ (20y)/(5b)
= [(20y + 6b)/(15y − 6b)] * [(5b)/(20y)]
= [(20y + 6b)(5b)]/[(15y − 6b)(20y)]
= (100y^2 + 30yb) / (300y^2 − 120by)
Since a:b = 6:5, this means that y = 5 and x = 6.
Therefore, we can substitute these values into the expression:
= (100(5)^2 + 30(5)(5)) / (300(5)^2 − 120(5)(5))
= (100(25) + 30(25)) / (300(25) − 120(25))
= (2500 + 750) / (7500 − 3000)
= 3250 / 4500
Simplifying this fraction by dividing both the numerator and denominator by 250, we get:
= 13 / 18
So the value of the expression is 13/18.
None of the given options match this result, so none of the provided options is the correct answer.
To find the value of the given expression, we first need to simplify it step by step.
Given: a:b = 6:5
Let's assume a = 6x and b = 5x, where x is a common factor for a and b.
We can rewrite the expression (4a + 6b/3a - b) ÷ (4a/5b) as:
= ((4 * 6x) + (6 * 5x))/(3 * 6x - 5x) ÷ (4 * 6x)/(5 * 5x)
= (24x + 30x)/(18x - 5x) ÷ (24x)/(25x)
= 54x/(13x) ÷ (24x)/(25x)
= 54/13 ÷ 24/25
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
= 54/13 * 25/24
= (54 * 25)/(13 * 24)
= 1350/312
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 78.
= (1350/78) / (312/78)
= 17.3077 / 4
= 4.32692
Rounded to two decimal places, the value of the expression is 4.33.
Therefore, the answer is not among the given options.