Question

A rocket is divided into three sections. The top section is one-eighth the length of the bottom section. The middle section is one-half the length of the bottom section. The total length of the rocket is 312ft. Find the length of the top section.

Answer 1

Answer:

312 ft

Step-by-step explanation:

The steps are as follows :

1. The problem can be described as an equation

$x + \frac{1}{2}x + \frac{1}{8}x = 312$

2. Convert all values on the left side into their equivalent fractional values

$\frac{8}{8}x + \frac{4}{8}x + \frac{1}{8} x = 312$

3. Combine like terms

$\frac{13}{8} x = 312$

4. Multiply both sides by the reciprocal of 13/8 to isolate variable X

$concept \: \: \: ({ \frac{8}{13} \times \frac{13}{8} }) = 1$

$\frac{8}{13} \times \frac{13}{8}x = 312 \: \times \frac{8}{13}$

5. Simplify

$x = 192$

6. Check answer by using it in the original equation

$(192) + \frac{1}{2}(192) + \frac{1}{8} (192) = 312$