this has a y intercept of +2
the line goes up 1 to the right 2 so m = 1/2
the equation of a line in slope intercept form is
y = mx+b
y = 1/2 x + 2
<span>(a) $7.04
(b) 704/1599
(c) 0.44
(d) 14
(e) $98.56
(a) How much profit does Lucy earn when she sells a necklace?
Since the problem states that her profit is the sale price minus the cost of materials and labor, we have the following equation.
P = $15.99 - $3.38 - $5.57
P = $12.61 - $5.57
P = $7.04
So her profit is $7.04 per necklace.
(b) Write a fraction of the profit per sale price of the necklace. Record your answer as a fraction using whole numbers.
The raw fraction is 7.04/15.99, to get rid of the decimal point, multiply top and bottom by 100, getting 704/1599.
The prime factors of 704 are 2,2,2,2,2,2,11 and the prime factors of 1599 are 3,13,41. Since neither 704, nor 1599 share any common factors, the fraction can't be reduced and the final answer is 704/1599.
(c) What decimal of every dollar of the sale price of the necklace is profit using the fraction from Part (b)?
Pardon the lack of formatting
704/1599 = 0.4403
Rounded to the nearest hundredth gives 0.44
(d) Lucy collected $223.86 selling necklaces at a craft fair. How many necklaces did Lucy sell? Show your work.
This question is asking for total cost. So divide the $223.86 by the sale price of $15.99.
$223.86 / $15.99 = 14
14 necklaces were sold.
(e) How much profit did she earn from the number of necklaces she sold? Show your work.
Since we know from (a) that she has $7.04 profit per necklace, just multiply the amount of profit by the number sold. So
$7.04 * 14 = $98.56</span>
Answer:
The system of linear inequalities to model the situation is written as:
x + y ≥ 5..... Equation 1
4x + 10y ≤ 100..... Equation 2
Step-by-step explanation:
Let
The number is soil = x
The number of plants = y
You are buying plants and soil for your garden.
You want to buy at least 5 plants
At least = greater than or equal to with the inequality sign(≥)
Hence:
x + y ≥ 5..... Equation 1
The soil cost $4 per bag and the plants cost $10 each and can spend no more than $100.
No more than means Less than or equal to with the inequality sign( ≤ )
Hence:
$4 × x +$10 × y ≤ $100
= 4x + 10y ≤ 100..... Equation 2
Therefore, the system of linear inequalities to model the situation is written as:
x + y ≥ 5..... Equation 1
4x + 10y ≤ 100..... Equation 2
