audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all…

audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (-1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)

audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (-1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)

Answer

Explanation:

Step1: Set up the inequality

The total weight of grapes is $x + y$, and she has less than 5 pounds of grapes, so the inequality is $x + y<5$. Also, since $x$ and $y$ represent weights of grapes, $x\geq0$ and $y\geq0$.

Step2: Check each option

Option 1: $(- 1,2)$

Since $x=-1<0$, it is not a reasonable solution as weight cannot be negative.

Option 2: $(1,3.5)$

Calculate $x + y=1 + 3.5=4.5<5$ and $x = 1\geq0$, $y = 3.5\geq0$, so it is a reasonable solution.

Option 3: $(2,2)$

Calculate $x + y=2+2 = 4<5$ and $x = 2\geq0$, $y = 2\geq0$, so it is a reasonable solution.

Option 4: $(4.5,0.5)$

Calculate $x + y=4.5+0.5 = 5$, but the inequality is $x + y<5$, so it is not a reasonable solution.

Option 5: $(5,0)$

Calculate $x + y=5+0 = 5$, but the inequality is $x + y<5$, so it is not a reasonable solution.

Answer:

$(1,3.5),(2,2)$