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.
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
(4a + 6b)/(3a − b) ÷ (4a/(5b)) = 225/52
Still not one of the choices ...
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 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.