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.
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
1 answer