Xero had

Xero had a piece of ribbon. He used 0.4 of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed for a large box is 3 times the length of ribbon needed for a small box. Xero used 5/6 of the remaining ribbon to decorate the presents.

a) What fraction of the ribbon did Xero use to tie one small box?
b) The length of the ribbon used for decorating the present was 7.65 m longer than the length of the ribbon used to tie one small box. What was the length Xero had at first?

Correct answer:

a =  1/20
s =  76.5 m

Step-by-step explanation:

$$\begin{gathered} 0.4=2a+2b \\ b=3a \\ 0.4=2\cdot a+2\cdot b \\ b=3\cdot a \\ 2a+2b=0.4 \\ 3a-b=0 \\ Pivot:Row1\leftrightarrow Row2 \\ 3a-b=0 \\ 2a+2b=0.4 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3a-b=0 \\ 2.67b=0.4 \\ b=\frac{0.4}{2.66666667}=0.15 \\ a=\frac{0+b}{3}=\frac{0+0.15}{3}=0.05=\frac{1}{20} \\ a=\frac{1}{20}=0.05 \\ b=\frac{3}{20}=0.15 \end{gathered}$$

$$\begin{gathered} b\cdot s=7.65+a\cdot s \\ 0.15\cdot s=7.65+0.05\cdot s \\ 0.1s=7.65 \\ s=\frac{7.65}{0.1}=76.5 \\ s=\frac{153}{2}=76.5=\frac{153}{2}\text{m}=76.5\text{m} \end{gathered}$$

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