eula needs to buy binders that cost $4 each and notebooks that cost $2 each. she has $20. the graph of the…

eula needs to buy binders that cost $4 each and notebooks that cost $2 each. she has $20. the graph of the inequality 4x + 2y ≤ 20, which represents the situation, is shown. what is the greatest number of binders eula can buy? what is the greatest number of notebooks eula can buy? if eula buys 7 notebooks, what is the greatest number of binders she can buy?

eula needs to buy binders that cost $4 each and notebooks that cost $2 each. she has $20. the graph of the inequality 4x + 2y ≤ 20, which represents the situation, is shown. what is the greatest number of binders eula can buy? what is the greatest number of notebooks eula can buy? if eula buys 7 notebooks, what is the greatest number of binders she can buy?

Answer

Answer:

  • What is the greatest number of binders Eula can buy? 5
  • What is the greatest number of notebooks Eula can buy? 10
  • If Eula buys 7 notebooks, what is the greatest number of binders she can buy? 1

Explanation:

Step1: Encontrar el máximo de encuadernaciones

Para encontrar el máximo número de encuadernaciones, suponemos que no compra cuadernos ($y = 0$). Sustituimos $y = 0$ en la desigualdad $4x+2y\leq20$. Obtenemos $4x\leq20$, entonces $x\leq\frac{20}{4}=5$.

Step2: Encontrar el máximo de cuadernos

Para encontrar el máximo número de cuadernos, suponemos que no compra encuadernaciones ($x = 0$). Sustituimos $x = 0$ en la desigualdad $4x + 2y\leq20$. Obtenemos $2y\leq20$, entonces $y\leq\frac{20}{2}=10$.

Step3: Calcular el número de encuadernaciones con 7 cuadernos

Si $y = 7$, sustituimos en la desigualdad $4x+2y\leq20$. Tenemos $4x+2\times7\leq20$, es decir $4x + 14\leq20$. Restando 14 de ambos lados, $4x\leq20 - 14=6$. Entonces $x\leq\frac{6}{4}=1.5$. Como $x$ es el número de encuadernaciones (un número entero), el máximo valor de $x$ es 1.