For their homecoming​ parade, the students of​ U-Math have created a colorful​ banner, 57 meters in​ length, that is made of two pieces of parachute material. The short piece is 23 meters shorter than the long piece. Find the length of each piece. Length of the long piece equals

Accepted Solution

Answer: [tex]Length\ of\ the\ long\ piece=40\ meters\\\\Length\ of\ the\ short\ piece=17\ meters[/tex]Step-by-step explanation: Let be "s" the length in meters of the short piece and "l" the lenght in meters of the long piece. Set up a system of equations: [tex]\left \{ {{s+l=57} \atop {s=l-23}} \right.[/tex] Apply the Substitution Method to solve the system. Substitute the second equation into the first equation and solve for "l": [tex](l-23)+l=57\\\\2l=80\\\\l=\frac{80}{2}\\\\l=40[/tex] Susbstitute the value of "l" into the second equation in order to find the value of "s". This is: [tex]s=40-23\\\\s=17[/tex]