Solve Algebra Ratio Problem: Find (5x+4):(4x-1)
Solving for x
We are given the ratio equation:
\( \frac{4x + 5}{3x + 11} = \frac{13}{17} \)
To solve for 'x', we cross-multiply:
\( 17(4x + 5) = 13(3x + 11) \)
Expand both sides:
\( 68x + 85 = 39x + 143 \)
Rearrange the terms to isolate 'x':
\( 68x - 39x = 143 - 85 \)
Simplify the equation:
\( 29x = 58 \)
Solve for 'x':
\( x = \frac{58}{29} \)
\( x = 2 \)
Calculating the Required Ratio
Now, we need to find the ratio (5x + 4) : (4x - 1) using the value \(x = 2\).
Substitute \(x = 2\) into the expression:
First part of the ratio:
\( 5x + 4 = 5(2) + 4 = 10 + 4 = 14 \)
Second part of the ratio:
\( 4x - 1 = 4(2) - 1 = 8 - 1 = 7 \)
The required ratio is \(14 : 7\).
Simplify the ratio:
\( 14 : 7 = \frac{14}{7} = \frac{2}{1} \)
So, the ratio is \(2 : 1\).
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