If r=t/2 and t=w/2, what is (r+w) in terms of t?
(A)t
(B)t^2
(C)3t/2
(D)5t/2
(e)5t/4
Please show work. Thanks.
The answer would be (D)
get rid of the denominator... 2t=w
add equations... r+w=t/2+ 2t
find common denominator... t/2+ 4t/2
answer... r+w= 5t/2
To find the value of (r+w) in terms of t, we need to substitute the given expressions for r and t into the equation.
Given:
r = t/2 ---- equation (1)
t = w/2 ---- equation (2)
Substituting equation (2) into equation (1) for r:
r = (w/2)/2 [substituting t = w/2]
r = w/4
Now, we can substitute the value of r back into the original equation to get (r+w) in terms of t:
(r+w) = (w/4) + w
Combining the fractions:
(r+w) = (w+4w)/4
(r+w) = 5w/4
Since we want the answer in terms of t, we need to express w in terms of t. We can use equation (2) to solve for w:
t = w/2
Rearranging the equation to solve for w:
w = 2t
Substituting w = 2t back into (r+w):
(r+w) = 5(2t)/4
(r+w) = 10t/4
Simplifying the fraction:
(r+w) = 5t/2
Therefore, the correct answer is option (D): 5t/2.
from the second,
w = 2t
so r+w = t/2 + 2t
= 3t/2 after finding a common denominator