Alice buys some inexpensive bracelets and necklaces as party favors for her jewelry showing. She pays $8 for each necklace (N) a
nd $7 for each bracelet (B). She spends less than $120. Which inequality models this situation? A) 7B + 8N ≤ 120
B) 7B + 8N > 120
C) 7B + 8N ≥ 120
D) 7B + 8N < 120
The total amount of the bracelets and necklaces is less than $120, so if you add the price of each necklace ($8) and the price of each bracelet ($7), it will be <$120.
We can convert the first equation to the same form as the second (y=mx+b, or slope-intercept).
12x +3y = 12
3y = -12x +12
y = -4x +4
Comparing the simplified first equation y = -4x +4 to the second equation y = -4x + 5, we see that both have the same slope (m = -4), but different y-intercepts (b = 4, b = 5). This means they are parallel lines, or an inconsistent system. There are no solutions.</span>