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

3 answers

To simplify this expression, we need to substitute the given ratio.

Given: a:b = 6:5

Let's express a in terms of b using this ratio:
a = (6/5)b

Now, let's substitute this value of a in the expression (4a + 6b)/(3a - b):
(4((6/5)b) + 6b)/(3((6/5)b) - b)

Simplifying further:
((24/5)b + 6b)/((18/5)b - b)

((24/5 + 30/5)b)/((18/5 - 5/5)b)

(54/5b)/(13/5b)

Simplifying further, we divide the numerator by the denominator:
(54/5b) * (5b/13)

The b terms cancel out, leaving us with:
54/13

Therefore, the value of the expression is 54/13.

None of the given options match this result.
(4a + 6b)/(3a − b) ÷ (4a/(5b)) = 225/52
Still not one of the choices ...
Apologies for the mistake in the initial response.

To find the value of the expression, let's substitute the given ratio:

Given: a:b = 6:5

Let's express a in terms of b using this ratio:
a = (6/5)b

Now, let's substitute this value of a in the expression (4a + 6b)/(3a - b) ÷ (4a/(5b)):
((4((6/5)b) + 6b)/(3((6/5)b) - b)) ÷ (4((6/5)b)/(5b))

Simplifying further:
((24/5)b + 6b)/((18/5)b - b) ÷ (24/5b)/(5b)

((24/5 + 30/5)b)/((18/5 - 5/5)b) ÷ (24/5b)/(5b)

(54/5b)/(13/5b) ÷ (24/5b)/(5b)

To divide fractions, we multiply by the reciprocal of the denominator:
(54/5b) * (5b/13) * (5b/24) * (5b/5b)

The b terms cancel out, leaving us with:
(54 * 5b * 5b) / (5b * 13 * 24 * 5b)

Simplifying further, the b terms cancel out:
(54 * 5 * 5) / (13 * 24 * 5)

(1350)/(3120) = 225/520

Therefore, the value of the expression is 225/520.

None of the given options match this result.