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If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?
- a)44 : 23
- b)23 : 45
- c)65 : 33
- d)46 : 25
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?a)44...
Given:
t : u = 7 : 4
Formula Used:
(7t + 4u) : (7t - 4u)
Calculation:
Let t = 7k and u = 4k, where k is a constant.
So, 7t = 7 × 7k = 49k
4u = 4 × 4k = 16k
⇒ (7t + 4u) = 49k + 16k = 65k
⇒ (7t - 4u) = 49k - 16k = 33k
Therefore, (7t + 4u) : (7t - 4u) = 65k : 33k = 65 : 33
The value of (7t + 4u) : (7t - 4u) is 65 : 33.
Most Upvoted Answer
If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?a)44...
Understanding the Ratio
Given the ratio t : u = 7 : 4, we can express t and u in terms of a single variable. Let:
- t = 7x
- u = 4x
where x is a common multiplier.
Calculating 7t + 4u
Now, we substitute t and u into the expression 7t + 4u:
- 7t = 7(7x) = 49x
- 4u = 4(4x) = 16x
Now, adding these:
- 7t + 4u = 49x + 16x = 65x
Calculating 7t - 4u
Next, we compute 7t - 4u:
- 7t = 49x
- 4u = 16x
Now, subtracting these:
- 7t - 4u = 49x - 16x = 33x
Finding the Ratio
Now, we need to find the ratio of (7t + 4u) to (7t - 4u):
- (7t + 4u) : (7t - 4u) = 65x : 33x
The x cancels out, giving us:
- 65 : 33
Final Result
Thus, the value of (7t + 4u) : (7t - 4u) is 65 : 33, which corresponds to option 'C'.
Given the ratio t : u = 7 : 4, we can express t and u in terms of a single variable. Let:
- t = 7x
- u = 4x
where x is a common multiplier.
Calculating 7t + 4u
Now, we substitute t and u into the expression 7t + 4u:
- 7t = 7(7x) = 49x
- 4u = 4(4x) = 16x
Now, adding these:
- 7t + 4u = 49x + 16x = 65x
Calculating 7t - 4u
Next, we compute 7t - 4u:
- 7t = 49x
- 4u = 16x
Now, subtracting these:
- 7t - 4u = 49x - 16x = 33x
Finding the Ratio
Now, we need to find the ratio of (7t + 4u) to (7t - 4u):
- (7t + 4u) : (7t - 4u) = 65x : 33x
The x cancels out, giving us:
- 65 : 33
Final Result
Thus, the value of (7t + 4u) : (7t - 4u) is 65 : 33, which corresponds to option 'C'.
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If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t - 4u)?a)44 : 23b)23 : 45c)65 : 33d)46 : 25Correct answer is option 'C'. Can you explain this answer?
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