using a graph to solve a problem\neula needs to buy binders that cost $4 each and notebooks that cost $2…

using a graph to solve a problem\neula 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.\nwhat is the greatest number of binders eula can buy?\nwhat is the greatest number of notebooks eula can buy?\nif eula buys 7 notebooks, what is the greatest number of binders she can buy?

using a graph to solve a problem\neula 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.\nwhat is the greatest number of binders eula can buy?\nwhat is the greatest number of notebooks eula can buy?\nif eula buys 7 notebooks, what is the greatest number of binders she can buy?

Answer

Explanation:

Step1: Find max binders

Set number of notebooks $y = 0$ in $4x+2y\leq20$. Then $4x\leq20$, so $x\leq5$.

Step2: Find max notebooks

Set number of binders $x = 0$ in $4x + 2y\leq20$. Then $2y\leq20$, so $y\leq10$.

Step3: Find binders when $y = 7$

Substitute $y = 7$ into $4x+2y\leq20$, we get $4x+2\times7\leq20$, which simplifies to $4x+14\leq20$, then $4x\leq6$, and $x\leq1.5$. Since $x$ is number of binders (a non - negative integer), $x = 1$.

Answer:

5 10 1