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The ratio of two positive numbers is 3 to 4. If k is added to each num
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02 Feb 2021, 09:09
02 Feb 2021, 09:09
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The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k ?
A. 1
B. 13
C. 14
D. 18
E. 21
A. 1
B. 13
C. 14
D. 18
E. 21
The ratio of two positive numbers is 3 to 4. If k is added to each num
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02 Feb 2021, 09:17
02 Feb 2021, 09:17
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Ratio = 3:4
let's take no as 3x & 4x
k is added to each - new ratio = 4:5
\(\frac{3x+k}{4x+k}\) = \(\frac{4}{5}\)
15x + 5k = 16x + 4k
\(x = k\)
Sum = 117
3x + k + 4x + k = 117
7x + 2k = 117
7x + 2x = 117
9x = 117
\(x = 13 = k\)
Answer B
let's take no as 3x & 4x
k is added to each - new ratio = 4:5
\(\frac{3x+k}{4x+k}\) = \(\frac{4}{5}\)
15x + 5k = 16x + 4k
\(x = k\)
Sum = 117
3x + k + 4x + k = 117
7x + 2k = 117
7x + 2x = 117
9x = 117
\(x = 13 = k\)
Answer B
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Re: The ratio of two positive numbers is 3 to 4. If k is added to each num
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02 Feb 2021, 09:37
02 Feb 2021, 09:37
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Carcass wrote:
The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k ?
A. 1
B. 13
C. 14
D. 18
E. 21
A. 1
B. 13
C. 14
D. 18
E. 21
The ratio of two positive numbers is 3 to 4.
Let 3x = the smaller number
Let 4x = the larger number
Aside: Notice that this ensures that their ratio will equal 3/4, since 3x/4x = 3/4
If k is added to each number the new ratio will be 4 to 5 . . .
When k is added to each value, the NEW values are 3x + k and 4x + k
So, (3x + k)/(4x + k) = 4/5
Cross multiply to get: 16x + 4k = 15x + 5k
Rearrange terms to get: x = k
. . . and the sum of the numbers will be 117
The two NEW values are 3x + k and 4x + k
So, we can write: (3x + k) + (4x + k) = 117
Simplify to get 7x + 2k = 117
Since x = k , we can take the above equation and replace x with k to get...
7k + 2k = 117
Simplify: 9k = 117
Solve: k = 13
Answer: B
Cheers,
Brent
