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
(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.
To find the value of (4a + 6b/3a - b) ÷ (4a/5b), we need to substitute the given ratio into the expression and simplify it.
1. Given a:b = 6:5, we can assign values to a and b. Let's assume that a = 6x and b = 5x, where x is a constant.
2. Substituting the values of a and b into the expression, we have:
(4(6x) + 6(5x))/(3(6x) - 5x) ÷ (4(6x)/(5(5x)))
3. Simplifying the numerator, we have:
(24x + 30x)/(18x - 5x) ÷ (24x)/(25x)
4. Further simplifying, we get:
54x/13x ÷ 24x/25x
5. Dividing the fractions, we have:
(54x/13x) * (25x/24x)
6. Simplifying, we get:
(54 * 25)/(13 * 24)
7. Evaluating the expression, we have:
1350/312 = 4.3269
8. Rounding this value to two decimal places, we get:
4.33
Therefore, the value of (4a + 6b/3a - b) ÷ (4a/5b) is approximately 4.33.
The correct answer is not provided in the options.
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.