Definitions
A fixed value without a variable is called:
A constant.
There are two different music download companies that offer a monthly plan for downloading songs. S-Jams charges $1.29 per song plus $10 monthly fee. C-tunes charges $0.99 per song plus $16 monthly fee. After how many songs will the company’s plans cost the same?
Let x = number of songs
Equation: 1.29x+10=0.99x+16
Solution: x = 20 songs
Solve 8 + 4d = 5d
d = 8
2x – 6 ≥ 3x – 11
x ≤ 5
A principal of $300 was deposited in a savings account that pays 3.5 interest compounded yearly. Find the balance after 5 years.
$356.31
A letter or symbol that represents a number
Variable
Joshua is changing his cell phone service. One data package that he is interested in charges a set-up fee of $28 and $8 per month. The other data package has no set-up fee but charges $12 per month for the same plan. After how many months will both packages cost the same? Write an equation and solve.
Let x = number of months
Equation: 28 + 8x = 12x
Solution: x = 7 months
11x = 24 + 8x
x = 8
5x – 20 ≤ 2x + 1
x ≥ 3
Jessica opened a savings account with a one‐time deposit of $100. The savings account will pay 3.9% simple interest each year. How much interest will she earn after 32 months?
$10.40
A mathematical statement composed of algebraic and/or numeric expressions set apart by a symbol
Inequality
Jacob has a balance of $160 in her school lunch account, and he spends $10 per day for lunch. His sister Samantha has $40 in her lunch account, and she spends $20 per day for lunch. In how many days will Jacob’s lunch account balance be less then Samantha’s? Write an equation and solve.
Let x = number of days
Equation: 160 + 10x = 40 + 20x
Solution: x = 12 days
5p + 2 = 4p -1
p = -3
5c + 2 < 2c – 7
c < -3
Cheyenne opened a savings account with a one‐time deposit of $100. The savings account will pay 5% compound annually. How much money will she have after 3 years?
$115.76
The numerical factor of a term that contains a variable (a number multiplied by a variable)
Coefficient
You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long will it be before you and your sister have the same amount of money? Write an equation and solve.
Let x = number of weeks
Equation: 60 + 7x = 120 + 5x
Solution: x = 30 weeks
Solve 2(g + 8) = 4(g - 3)
g=14
-7 – e ≥ 3e + 11
e ≤ -4
Jamie wants to earn $500 in interest so she will have enough to pay a used car. She puts $2000 in to an account that earns 2.5 percent simple interest. How long will she need to leave her money in the account to earn $500 in interest?
10 years
These types of terms contain the same variables. Constants are also called this type of term.
Like Terms
Suppose you can rent a car for either $35 a day plus $0.40 a mile or for $20 a day plus $0.55 per mile. Write and solve an equation to find the number of miles that result in the SAME cost for one day.
Let x = number of miles in one day
Equation: 35 + 0.40x = 20 + 0.55x
Solution: x = 100 miles
Solve -6(n + 9) = 4(5n - 7)
n=-1
5x – 3 > 2(3 + x)
x > 3
Griffin opened two savings accounts with a one‐time deposit of $300 in each account. The first savings account will pay 5% simple interest each year. The second one will pay 5% compound annually. Which account will have the most money after 5 years. Explain your reasoning.
The second account will have $7.87 more after 5 years. The first account balance will be $375 and the second account balance will be $382.87.