Various Topics
Mathematicians are:
Smart but a little bit lazy
-7m = 63
m = -9
-w/2 = -16
-w = -32
Maria has 12 apples. She gives away some apples to her friend, and now she has 8 apples left. How many apples did Maria give away? Write the equation and solve for the variable.
Let x be the number of apples Maria gave away.
The equation is:
12 − x = 8
x = 12 − 8
x = 4
Step 1 in solving linear equations is:
Distribute!
The number that is multiplied by the variable.
numerical coefficient.
n/56 = -8
n = -448
4x − 8 = 16
x = 6
A book costs $15, and there is a 10% sales tax on the purchase. If you have $25, how much money will you have left after buying the book including tax?
The cost of the book including tax can be calculated as follows:
Sales tax: 10% of 15 = 0.10 × 15 = 1.50
Total cost of the book: 15 + 1.50 = 16.50
Amount left after purchase: 25 − 16.50 = 8.50
You will have $8.50 left after buying the book including tax.
Step 2 in solving linear equations is:
combine like terms
_____ means to put together; add.
What is combine?
-2k - 4 = 8
k = -6
7 − 3y = 1
Tom has a collection of 20 baseball cards. He receives xx more cards as a gift, which brings his total to 40 cards. If he then gives away 10 cards to his friends, how many cards does he have now?
Let x be the number of baseball cards Tom received.
The equation is:
20 + x = 40
x = 40 − 20
x = 20
After receiving the cards, Tom has 40 cards. If he gives away 10 cards:
40 − 10 = 30
Tom has 30 baseball cards now.
The name of 2 8th grade math teachers at St. Matt's
Who are Da Costa and Fortin.
The number that does not change in an expression.
h/-3 + 6 = -4
h = 30
3 (a − 4) + 2 = 5
a = 5
A school is organizing a field trip. The cost of the trip is $1200, which includes a fixed cost of $800 for the bus and $20 per student. If 30 students are going, how much will each student have to pay?
Let x be the number of students.
The cost equation is:
800 + 20x = 1200
20x = 1200 − 800
20x = 400
x = 400/20
x = 20
Each student pays:
Total cost per student: 1200/20 = 60
Each student will have to pay $60.
What are the 3 substeps in isolating the variable?
a. put the variables together
b. move the constants to the other side of the =
c. multiply or divide to make it a single Variable
The four steps to solving multi-equations are 1. ___ 2. ___ 3.____ 4._____.
The four steps to solving multi-equations are 1. Distributive Property 2. Combine like terms (get the variable on one side) 3. Get the variables on one side. 4. Solve.
-h/5 + 9 = 8
h = -5
5z + 2 = 3z + 18
A car rental company charges a flat fee of $50 plus $0.20 per km driven. If a customer paid $70, how many km did they drive?
Let m be the number of miles driven.
The equation is:
50 + 0.20m = 70
0.20m = 70 − 50
0.20m = 200
m = 20/0.20
m = 100
The customer drove 100 km.