Question

write a system of equations to describe the situation below, solve using any method, and fill in the blanks. the receivers for the somerville university football team are practicing running different routes on the field. they have to run a specific distance so that the quarterback knows exactly where to throw the ball. zachary ran 10 post routes and 11 slant routes, which meant he ran a total of 288 yards. fernando ran 16 post routes and 21 slant routes, which meant a total of 488 yards. how long is each route? a post route is yards long and a slant route is yards long.

Explanation:

Step1: Definir variables

Supongamos que la longitud de una ruta post sea \(x\) yardas y la longitud de una ruta slant sea \(y\) yardas.
Para Zachary: \(10x + 11y=288\)
Para Fernando: \(16x + 21y = 488\)

Step2: Resolver el sistema de ecuaciones

Multiplicamos la primera ecuación por \(16\) y la segunda por \(10\)
Primera ecuación multiplicada: \(160x+176y = 4608\)
Segunda ecuación multiplicada: \(160x+210y=4880\)
Restamos la primera ecuación multiplicada de la segunda:
\((160x + 210y)-(160x + 176y)=4880 - 4608\)
\(160x+210y - 160x - 176y=272\)
\(34y=272\)
\(y=\frac{272}{34}=8\)

Step3: Encontrar \(x\)

Sustituimos \(y = 8\) en la ecuación \(10x+11y = 288\)
\(10x+11\times8=288\)
\(10x+88 = 288\)
\(10x=288 - 88\)
\(10x=200\)
\(x = 20\)

Answer:

A post route is \(20\) yards long and a slant route is \(8\) yards long.