1. elijah gets 3% commission for every car he sells. if he sold several cars for $48,000, what would be his commission?
2. aaliyah buys 3 pairs of shoes at a yard sale for $15 each. if she restores them and sells them for $45 per pair, what is her profit?
3. the store increased the price from $40 to $52. find the percent increase.
4. the regular price of the hat was $36. if the hat was sold for $\frac{1}{4}$ off, find the sale price of the hat?
5. what percent of 60 is 39?
6. find the unit rate from this graph.
7. the philadelphia flyers were given two points for each win. is this a proportional relationship?
8. graph this relationship. is this proportional?
9. write an algebraic equation for the following table:
10. find the c.o.p. of this table:

Question

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Convert percentage to decimal
To find the commission, we first convert 3% to a decimal. 3% is equivalent to $0.03$ (since $3\%=\frac{3}{100} = 0.03$).
## Step2: Multiply by total sales
Elijah's total sales are $48,000$. So his commission is $48000	imes0.03$.
Calculating that: $48000	imes0.03 = 1440$.
# Answer:
\$1440

### Problem 2:
# Explanation:
## Step1: Calculate total cost
Aaliyah buys 3 pairs of shoes at \$15 each. So total cost is $3	imes15=\$45$.
## Step2: Calculate total revenue
She sells each pair for \$45, so total revenue is $3	imes45=\$135$.
## Step3: Calculate profit
Profit = Revenue - Cost. So profit is $135 - 45=\$90$.
# Answer:
\$90

### Problem 3:
# Explanation:
## Step1: Find the amount of increase
The original price is \$40, new price is \$52. The increase is $52 - 40=\$12$.
## Step2: Calculate percent increase
Percent increase is calculated as $\frac{	ext{Increase}}{	ext{Original Price}}	imes100\%$. So $\frac{12}{40}	imes100\%$.
Calculating that: $\frac{12}{40}=0.3$, and $0.3	imes100\% = 30\%$.
# Answer:
30%

### Problem 4:
# Explanation:
## Step1: Find the discount amount
The regular price is \$36, and the discount is $\frac{1}{4}$ off. So discount amount is $36	imes\frac{1}{4}=\$9$.
## Step2: Calculate sale price
Sale price = Regular price - Discount. So $36 - 9=\$27$.
# Answer:
\$27

### Problem 5:
# Explanation:
## Step1: Set up the percentage formula
To find what percent of 60 is 39, we use the formula $\frac{39}{60}	imes100\%$.
## Step2: Calculate the percentage
$\frac{39}{60}=0.65$, and $0.65	imes100\% = 65\%$.
# Answer:
65%

### Problem 6:
# Explanation:
## Step1: Identify two points from the graph
Looking at the graph, when hours = 1, miles = 6 (assuming the first point is (1,6), then (2,12), (4,24), (6,36), (8,48)). Wait, actually, from the graph, when hours = 1, miles = 6? Wait, no, let's check the coordinates. The first point (1,6)? Wait, the y - axis is miles, x - axis is hours. Let's take two points, say (1,6) and (2,12). The unit rate is the slope, which is $\frac{	ext{Change in Miles}}{	ext{Change in Hours}}$.
For (1,6) and (2,12), the change in miles is $12 - 6 = 6$, change in hours is $2 - 1 = 1$. So unit rate is 6 miles per hour. Wait, or looking at (8,48), $\frac{48}{8}=6$. So unit rate is 6 miles per hour.
# Answer:
6 miles per hour

### Problem 7:
# Explanation:
A proportional relationship can be written as $y = kx$, where $k$ is a constant. Let $y$ be the total points and $x$ be the number of wins. Here, $y = 2x$ (since 2 points per win). This is in the form $y = kx$ with $k = 2$, so it is a proportional relationship.
# Answer:
Yes

### Problem 8:
# Explanation:
First, we graph the points from the table: (1,4), (2,3), (3,2), (4,1). To check proportionality, a proportional relationship should pass through the origin and have a constant ratio (unit rate). Let's check the ratios: $\frac{4}{1}=4$, $\frac{3}{2}=1.5$, $\frac{2}{3}\approx0.67$, $\frac{1}{4}=0.25$. The ratios are not constant, and the line (when graphed) does not pass through the origin (if we extend the line, when minutes = 0, points would not be 0). So it is not proportional.
# Answer:
The graph is a line with points (1,4), (2,3), (3,2), (4,1). No, it is not proportional.

### Problem 9:
# Explanation:
Let's assume the equation is $y=mx + b$. Let's take two points, say (2, - 4) and (6,8).
## Step1: Calculate the slope (m)
$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8-(-4)}{6 - 2}=\frac{12}{4}=3$.
## Step2: Find the y - intercept (b)
Using point (2, - 4) and $y = 3x + b$. Plug in $x = 2$, $y=-4$: $-4=3	imes2 + b
ightarrow - 4=6 + b
ightarrow b=-10$.
Let's check with another point, (9,17): $y = 3	imes9-10=27 - 10 = 17$. Correct. (20,50): $3	imes20-10=60 - 10 = 50$. Correct. So the equation is $y = 3x-10$.
# Answer:
$y = 3x - 10$

### Problem 10:
# Explanation:
For a proportional relationship, the constant of proportionality (C.O.P.) is $\frac{y}{x}$. Let's check the ratios:
For (1,7): $\frac{7}{1}=7$
For (2,14): $\frac{14}{2}=7$
For (3,21): $\frac{21}{3}=7$
For (4,25): $\frac{25}{4}=6.25$
Wait, but the first three have a ratio of 7, but the fourth is different. Wait, maybe a typo? Wait, if we consider the first three, the C.O.P. is 7. But the fourth point (4,25) doesn't fit. But maybe the table has an error, or we consider the first three. Wait, the problem says "Find the C.O.P. of this table". But since the first three have a constant ratio of 7, maybe that's the intended C.O.P. (assuming the last point is a mistake). So C.O.P. is 7.
# Answer:
7

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Convert percentage to decimal

Step2: Multiply by total sales

Step1: Calculate total cost

Step2: Calculate total revenue

Step3: Calculate profit

Step1: Find the amount of increase

Step2: Calculate percent increase

Answer:

Problem 2: