Toán Lớp 6: Four similar pens and three similar pencils cost $18. Four similar rulers and three similar pencils cost $12. The cost of three such pe

Question

Toán Lớp 6:  Four similar pens and three similar pencils cost $18. Four similar rulers and three similar pencils cost $12. The cost of three such pens and three such rulers is $13.50. Find the cost of each pencil.

hienthucthu97 · Answer

Giải đáp:      The cost of pens, pencils, rulers respectively is: 3$; 2$ and 1,5$     Lời giải và giải thích chi tiết:     Call cost of a pen is: x($)   cost of a pencil is: y($)   cost of a ruler is: z($)   (x,y>0)   We have the equation:   $ begin{cases} 4x+3y=18(1)  3y+4z=12(2)  3x+3z=13,5(3)  end{cases}$   From (3) => x={13,5-3z}/3=4,5-z    Replace x in (1) => 18-4z+3y=18 => 3y-4z=0 (4)   Solve (2) and (4) => $ left  { {{3y+4z=12}  atop {3y-4z=0}}  right.$   =>$ left  { {{y=2}  atop {z=1,5}}  right.$   => x=4,5-z=4,5-1,5=3   Therefore, the cost of pens, pencils, rulers respectively is: 3$; 2$ and 1,5$