Question

svlc algebra 1a - standard (15260)
modeling with two - variable linear inequalities
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? choose two correct answers.
( (1, 3.5) )
( (-1, 2) )
( (2, 2) )
( (4.5, 0.5) )
( (5, 0) )

Explanation:

Step1: Define the inequality

The total pounds of grapes is \( x + y \), and it's less than 5, so the inequality is \( x + y < 5 \). Also, since \( x \) and \( y \) represent pounds of grapes, \( x \geq 0 \) and \( y \geq 0 \) (you can't have negative pounds of grapes).

Step2: Test each point

• For \( (1, 3.5) \): \( 1 + 3.5 = 4.5 < 5 \), and \( x = 1 \geq 0 \), \( y = 3.5 \geq 0 \). Valid.
• For \( (-1, 2) \): \( x = -1 < 0 \), invalid (can't have negative pounds).
• For \( (2, 2) \): \( 2 + 2 = 4 < 5 \), \( x = 2 \geq 0 \), \( y = 2 \geq 0 \). Valid.
• For \( (4.5, 0.5) \): \( 4.5 + 0.5 = 5 \), but the inequality is \( < 5 \), so \( 5 \) is not less than \( 5 \). Invalid.
• For \( (5, 0) \): \( 5 + 0 = 5 \), same as above, \( 5 \) is not less than \( 5 \). Invalid.

Answer:

(1, 3.5), (2, 2)