A welder

A welder has two pieces of half-inch pipe, one of length 2 3/8 ft and another of length 3 7/8 ft.

What is the total length of the two welded together?
How much must be cut off if she needs a total length of 4 3/4 ft?

Correct answer:

t =  6 ¹⁄₄ = 25/4 ft
x =  1 ¹⁄₂ = 3/2 ft

Step-by-step explanation:

$$\begin{gathered} a=2\frac{3}{8}=2+\frac{3}{8}=\frac{2\cdot 8+3}{8}=\frac{16+3}{8}=\frac{19}{8}=2.375\text{ft} \\ b=3\frac{7}{8}=3+\frac{7}{8}=\frac{3\cdot 8+7}{8}=\frac{24+7}{8}=\frac{31}{8}=3.875\text{ft} \\ t=a+b=\frac{19}{8}+\frac{31}{8}=\frac{19+31}{8}=\frac{50}{8}=\frac{25}{4}\text{ft}=6\frac{1}{4}\text{ft}=6.25\text{ft} \end{gathered}$$

$x=t-4\frac{3}{4}=\frac{25}{4}-4\frac{3}{4}=\frac{25}{4}-\frac{19}{4}=\frac{25-19}{4}=\frac{6}{4}=\frac{3}{2}\text{ft}=1\frac{1}{2}\text{ft}=1.5\text{ft}$

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