Question $\frac{x+3}{x+4}=\frac{24}{27}$

Studdy Solution

STEP 1

1. The equation $\frac{x+3}{x+4}=\frac{24}{27}$ is a proportion.
2. We will use cross-multiplication to solve for $x$ .

STEP 2

1. Simplify the fraction on the right-hand side.
2. Cross-multiply to eliminate the fractions.
3. Solve the resulting linear equation for $x$ .

STEP 3

Simplify the fraction $\frac{24}{27}$ by finding the greatest common divisor of 24 and 27, which is 3. Divide both the numerator and the denominator by 3:
$\frac{24}{27} = \frac{24 \div 3}{27 \div 3} = \frac{8}{9}$

STEP 4

Cross-multiply to eliminate the fractions. This means multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal:
$(x+3) \cdot 9 = (x+4) \cdot 8$

STEP 5

Distribute the numbers on both sides of the equation:
$9(x+3) = 8(x+4)$
Expanding both sides:
$9x + 27 = 8x + 32$

STEP 6

Isolate $x$ by first subtracting $8x$ from both sides:
$9x - 8x + 27 = 32$ $x + 27 = 32$

STEP 7

Subtract 27 from both sides to solve for $x$ :
$x + 27 - 27 = 32 - 27$ $x = 5$
The value of $x$ is:
$\boxed{5}$

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