Fruit equation

Find how many peaches could be bought instead of buying one melon, one pear, one apple, and two plums if
we know that:
• Melon and plum cost the same as three apples
• if we subtract the price of a pear from the price of a peach, we get the price of a plum
• Two peaches and one pear stand together just like a melon and an apple
• Apple and pear stand together just like plum and peach together.

Correct answer:

x =  4

Step-by-step explanation:

$$\begin{gathered} m+s=3\cdot j \\ b-h=s \\ 2\cdot b+h=m+j \\ j+h=s+b \\ b=1 \\ 3j-m-s=0 \\ b-h-s=0 \\ 2b+h-j-m=0 \\ b-h-j+s=0 \\ b=1 \\ Pivot:Row1\leftrightarrow Row3 \\ 2b+h-j-m=0 \\ b-h-s=0 \\ 3j-m-s=0 \\ b-h-j+s=0 \\ b=1 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ b-h-j+s=0 \\ b=1 \\ Row4-\frac{1}{2}\cdot Row1\to Row4 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -1.5h-0.5j+0.5m+s=0 \\ b=1 \\ Row5-\frac{1}{2}\cdot Row1\to Row5 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -1.5h-0.5j+0.5m+s=0 \\ -0.5h+0.5j+0.5m=1 \\ Row4-Row2\to Row4 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -j+2s=0 \\ -0.5h+0.5j+0.5m=1 \\ Row5-\frac{-0.5}{-1.5}\cdot Row2\to Row5 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -j+2s=0 \\ 0.33333j+0.33333m+0.33333s=1 \\ Row4-\frac{-1}{3}\cdot Row3\to Row4 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -0.33333m+1.66667s=0 \\ 0.33333j+0.33333m+0.33333s=1 \\ Row5-\frac{0.33333333}{3}\cdot Row3\to Row5 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ -0.33333m+1.66667s=0 \\ 0.44444m+0.44444s=1 \\ Pivot:Row4\leftrightarrow Row5 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ 0.44444m+0.44444s=1 \\ -0.33333m+1.66667s=0 \\ Row5-\frac{-0.33333333}{0.44444444}\cdot Row4\to Row5 \\ 2b+h-j-m=0 \\ -1.5h+0.5j+0.5m-s=0 \\ 3j-m-s=0 \\ 0.44444m+0.44444s=1 \\ 2s=0.75 \\ s=\frac{0.75}{2}=0.375 \\ m=\frac{1-0.44444444444444s}{0.44444444}=\frac{1-0.44444444\cdot 0.375}{0.44444444}=1.875 \\ j=\frac{0+m+s}{3}=\frac{0+1.875+0.375}{3}=0.75 \\ h=\frac{0-0.5j-0.5m+s}{-1.5}=\frac{0-0.5\cdot 0.75-0.5\cdot 1.875+0.375}{-1.5}=0.625 \\ b=\frac{0-h+j+m}{2}=\frac{0-0.625+0.75+1.875}{2}=1 \\ b=1 \\ h=\frac{5}{8}=0.625 \\ j=\frac{3}{4}=0.75 \\ m=\frac{15}{8}=1.875 \\ s=\frac{3}{8}=0.375 \\ x=m+h+j+2\cdot s=1.875+0.625+0.75+2\cdot 0.375=4 \end{gathered}$$

Try another example