Math 15 - Equations

Solving

100

-5p + 1 = 6

p = -1

200

4(6 + 5x) = 124

x = 5

300

-93 = 7(-3k - 8) + 5

k = 2

400

172 = 5(4a + 6) + 2

a=7

500

Verify if x = 3 is a solution to the equation:

4x - 17 = -2x + 32

Show if LS = RS?

NO! Verification shows LS does not equal RS (-5 does not equal 26)
(Solution = 49/6)

Rearranging

100

Solve P = a + b + c for the variable b

b = P - a - c

200

Solve E=IR for the variable R

R=E/I

300

Solve P= (R-C)/n for the variable R

R= Pn + C

400

Solve A=(1/2)h(b₁+b₂) for b₂

b₂=(2A/h)-b₁

500

Isolate for x in: 

y = (1/2)xz²

x = 2y/z²

Application

100

The larger of two numbers is eight more than 6 times the smaller. Their sum is 148, what are the numbers?

The number are 20 and 128. 

200

When the smaller of two consecutive integers is added to 9 times the larger, the result is 109. Find the two integers.

The consecutive numbers are 10 and 11. 

300

The length of a rectangular field is 22 meters longer than 3 times the width. If the perimeter of the field is 132 meters, what are the dimensions of the field?

The dimensions are 11m by 55m.

400

Matt has a bag that contains 20 coins, all of which are either quarters or dimes. If the total value is $3.50, how many coins of each coin does Matt have?

Matt has 10 quarters and 10 dimes. 

500

Amy is 6 years older than Brad. In 12 years the sum of their ages will be 60. How old is Brad today?

Today, Brad is 15 years old. 

Fractions!

100

20/3 = x + 19/6

x = 7/2

200

-61/12 = b - 4/3

b=-15/4

300

9/4 = -3n/2 + 19/4

n = 5/3

400

7/4(b-1) = 7/8

b = 3/2

500

5/7(3/2 + n) = 145/84

n = 11/12

System of Equations

100

y=-2
y = 4x + 6

(-2,-2)

200

y=3x
y = -5x – 8

(-1,-3)

300

y = -4x+5 

y = 2x – 7

(2, -3)

400

x=3y–1 

x + 2y = 9

(5, 2)

500

x–y=2
4x – 3y = 11

(5, 3)