Question

select the correct answer(s) in each table.
an art store offers prints in two sizes. the store earns $15 on each small print sold and $25 on each large print sold. the owner needs to make a daily profit of at least $700 in order to cover costs. due to equipment limitations, the number of small prints made must be more than three times the number of large prints.
given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation.
inequality options
$x + y \leq 60$ $15x + 25y < 700$ $x > 3y$
$15x + 25y \geq 700$ $y > 3x$ $x + 3y \geq 60$
which combinations of small prints and large prints satisfy this system?
combination options
(45,10) (35,15) (30,10) (40,5)

Explanation:

Step1: Identify constraints from text

1. Total prints sold: $x + y \leq 60$
2. Minimum daily profit: $15x + 25y \geq 700$
3. Equipment limit: $x > 3y$

Step2: Test each combination on constraints

For (45,10):

• $45+10=55 \leq 60$: True
• $15(45)+25(10)=675+250=925 \geq 700$: True
• $45 > 3(10)=30$: True

For (35,15):

• $35+15=50 \leq 60$: True
• $15(35)+25(15)=525+375=900 \geq 700$: True
• $35 > 3(15)=45$: False

For (30,10):

• $30+10=40 \leq 60$: True
• $15(30)+25(10)=450+250=700 \geq 700$: True
• $30 > 3(10)=30$: False

For (40,5):

• $40+5=45 \leq 60$: True
• $15(40)+25(5)=600+125=725 \geq 700$: True
• $40 > 3(5)=15$: True

Answer:

Correct Inequalities:

$x + y \leq 60$, $15x + 25y \geq 700$, $y > 3x$

Valid Combinations:

(45,10), (40,5)