Question

5.
topic 2 systems of linear equations
number of flower wreaths
wreaths: x; income (dollars): 37x; production cost (dollars): 12x + 500; profit (dollars): 25x - 500
wreaths: 0; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
wreaths: 10; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
wreaths: 12; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
wreaths: 14; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
wreaths: 20; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
wreaths: 100; income (dollars): blank; production cost (dollars): blank; profit (dollars): blank
the productions cost and the income are equivalent when there are select flower wreaths produced.

Explanation:

Step1: Calculate Income for each x

Substitute each x into $37x$:

• $x=0$: $37(0)=0$
• $x=10$: $37(10)=370$
• $x=12$: $37(12)=444$
• $x=14$: $37(14)=518$
• $x=20$: $37(20)=740$
• $x=100$: $37(100)=3700$

Step2: Calculate Production Cost for each x

Substitute each x into $12x+500$:

• $x=0$: $12(0)+500=500$
• $x=10$: $12(10)+500=620$
• $x=12$: $12(12)+500=644$
• $x=14$: $12(14)+500=668$
• $x=20$: $12(20)+500=740$
• $x=100$: $12(100)+500=1700$

Step3: Calculate Profit for each x

Substitute each x into $25x-500$:

• $x=0$: $25(0)-500=-500$
• $x=10$: $25(10)-500=-250$
• $x=12$: $25(12)-500=-200$
• $x=14$: $25(14)-500=-150$
• $x=20$: $25(20)-500=0$
• $x=100$: $25(100)-500=2000$

Step4: Find break-even (income=cost)

Set $37x=12x+500$, solve for x:
$37x-12x=500$
$25x=500$
$x=\frac{500}{25}=20$

Answer:

Completed Table:

Number of Flower Wreaths	Income (dollars)	Production Cost (dollars)	Profit (dollars)
10	370	620	-250
12	444	644	-200
14	518	668	-150
20	740	740	0
100	3700	1700	2000

The production cost and income are equivalent when there are 20 flower wreaths produced.