Constant of Proportionality
How do you solve for k?
What is your k-value for the following equations?
y = x
y = 3.5 x
k = y/x
k = 1
k = 3.5
Find the tax amount given the original price and the tax rate,
$73.81, 7.5%
$73.81 x 0.075 = $5.54
What is my Interest formula?
I = Prt
Give the rate in miles per hour.
John jogs 8 feet per second.
5.5 miles per hour
Solve:
-15 - (-45) =
two negatives make a positive
-15 + 45 = (different signs mean difference, subtract)
45 - 15 = 30 (take sign of bigger number)
30
What two things does a graph need to be proportional?
Straight line
Through the origin (0,0)
The store has a shirt priced for $25.89. They are running a sale for 15% off. How much would you pay for the shirt?
100% - 15% = 85% or 0.85 (**shortcut)
$25.89 x 0.85 = 20.0065
$20.0065
$20.01
What is my Commission formula?
Total Earnings = base salary + commission + fees
A map has a scale of 1 in : 10 mi. Find the distance on the map between two cities that lie 147 miles apart.
147 miles x 1 in = 147 miles/10miles = 14.7 in
14.7 in
(cancel out the units!)
Solve:
-10 - (-3) =
two negatives make a positive
-10 + 3 = (different means difference, subtract)
10 - 3 = -7 (take sign of bigger number)
-7
What is the original equation that x can be plugged into?
y = kx
A store buys bracelets for $10. They mark them up to $18 to sell. What is the percent markup?
change/original
18-10 = 8
8/10 = 0.8
0.8
80%
A loan officer makes $15 per hour working 2,000 hours each year. She also gets a fee of $35 for each loan she processes. If she processes 75 loans a month, what are her total earnings for the year?
Earnings = salary + commission + fees
Earnings = (2,000)(15) + (75)(12)(35)
$61,500
A gardener plants 2/6 of a row of carrots in 1/2 of an hour. How many rows would they plant in 1 hour?
Ratio
rows:time rows/time
2/6 divided by 1/2
2/3
Solve:
20 - (-40) - 15 + 30 =
Written as addition:
20 + 40 + (-15) + 30 =
60 + (-15) = 45 (different means subtract)
45 + 30 = 75
75
What all is considered to be a k-value?
*hint: there are 4 of them
The price of a used car is $12,000 including tax. The sales tax rate is 9%.
What is the original price of the item?
100% + 9% = 109% pr 1.09
12,000 / 1.09 = 11,009.17
$11,009.17
A literary agent makes $30,000 a year plus 13% commission on the sales of her clients' books to publishers. The agent sold 4 books for $175,000 each for her clients this year. Find her total earnings.
Total Earnings = Salary + commission + fees
Earnings = 30,000 + (175,000)(4)(0.13)
$121,000
An IT guy fixes 1/5 of his job in 1/3 of an hour. At this rate, how long will it take for him to complete the entire job?
Ratio
time:job
1/3 divided by 1/5
1 2/3
Change the equation into addition and solve.
15 - 6 - 8 - (-2) =
Written as addition:
15 + (-6) + (-8) + 2 =
15 - 6 = 9
9 + (-8) = 1
1 + 2 = 3
3
Determine if (3,7),(6,14),(9,22),(12,28) is proportional.
No
k = y/x
Find the total amount given the original price and tip rate.
$22.22, 10%
**Shortcut
100% + 10 % = 110% or 1.10
$22.22 x 1.10 = $24.44
A savings account pays an annual simple interest rate of 1.5%.
A. How much interest would you earn in 1 year on $2,000?
B. What would be the balance in the account after 5 years?
C. How long would it take to earn $500 or more in interest?
A. I = (2,000)(0.015)(1) = $30
B. $30 x 5 = $150 ; $150 + $2,000 = $2,150
C. I = Prt
500 = (2,000)(0.015)(t)
500 = 30 x (t)
500/30 = 16.6 years or 17 years
Tony ran 4/5 of a mile in 1/5 of an hour. Write an equation for the distance in miles per hour that she ran if she ran at a constant rate.
4/5 miles : 1/5 hours = 4
Write as a fraction and KCF
Write as an equation:
y = kx
y = 4x
Chane the equation into addition and solve.
3 + 2 - 7 + 3 - 2 =
Rewritten as addition:
3 + 2 + (-7) + 3 + (-2) =
5 + (-7) = -2
-2 + 3 = 1
1 + (-2) = -1
-1