OBJECTIVE: Students will be able to______.

The “Less than” rule

Example: Eight less unknown number
/ Example: 8 less than a number

Guided Practice: Write the equations as seen on the board

1.4.

2.5.

3.6.

Quantity & Value System Problems

Ex 1) Step 1: Define variables
The length of a rectangle is three times its width. If the perimeter of the rectangle is 120 centimeters, which system of equations can be used to find the dimensions of the rectangle?
Let x = ______
y = ______
Step 2:
Equation 1:
Step 3:
Equation 2: / #2) The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Write a system of equations to represent the costs of both.
Let e = ______
u = ______
Equation 1:
Equation 2: / #3) The perimeter of a rectangular wooden deck is 90 feet. The deck’s length, l, is 5 feet less than 4 times
its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of thewooden deck?
Let l = ______
w = ______
Equation 1:
Equation 2:

Independent Practice

Complete at least 6 questions correctly.

1) Alexis bought pizza and soda for the ski club meeting. For one meeting she bought 3 pizzas and 18 sodas for $24. The next meeting she bought 3 pizzas and 20 sodas for $26. Write a system of equations to represent the cost of each transaction.
Let p = ___# of pizzas______
s = _____#of sodas______
Equation 1: 3p + 18s = 24
Equation 2:3p + 20s = 26 / 2) Translate to slope intercept form.

y = .5x
or
y = ½ x
3)At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, Write a system of equations that can be used to represent how many of each Carla purchased
Let m= math textbook
Let n = novel
m + n = 54
3n +8 = m / 4) Mr. Horan empties out his pockets at the end of day and takes out a bunch of nickels and quarters. He has $3.75 in change in his pocket. He has 4 less quarters than twice the number of nickles. Write a system of equations that could be used to find n, the number of nickels he has, and q, the number of quarters.
Let n = number of nickels
Let q = number of quarters
n + d = 3.75
4 - 2n = q
5) The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. Write a system of equations to represent the costs of both. / 6) Isolate the x variable by itself (i.e. x = ??????):

X = 6 + 2y
7) Graph the line from problem 6 /
  1. 8) A breakfast menu lists 2 eggs with 1 sausage patty for $2.23 and 3 eggs with 2 sausage patties for $3.76. Write a system of equations to represent the costs of both.

Name: ______Period: ______

DOL: Writing Systems of Equations

  1. The perimeter of a rectangular volleyball court is 180 feet. The court’s width, w, is half its length, l.Which system of linear equations could be used to determine the dimensions, in feet, of the volleyballcourt?

A l + w = 180B 2l + 2w = 180

w = lw = l

C l + w = 180D 2l + 2w = 180

l = wl = w

  1. The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. Which system of equations could be used to find the number of sundaes, s, and banana splits, b, that the shop sold that day?

A2s + 3b = 156C 2s + 3b = 8

s = b + 8s = b + 156

B 2b + 3s = 156D 2s + 3b = 156

s + b = 8b − s = 8

Name: ______Period: ______

DOL: Writing Systems of Equations

  1. The perimeter of a rectangular volleyball court is 180 feet. The court’s width, w, is half its length, l.Which system of linear equations could be used to determine the dimensions, in feet, of the volleyballcourt?

A l + w = 180B 2l + 2w = 180

w = lw = l

C l + w = 180D 2l + 2w = 180

l = wl = w

  1. The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. Which system of equations could be used to find the number of sundaes, s, and banana splits, b, that the shop sold that day?

A2s + 3b = 156C 2s + 3b = 8

s = b + 8s = b + 156

B 2b + 3s = 156D 2s + 3b = 156

s + b = 8b − s = 8

  1. Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 108 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?

A l + t = 108C l + t = 108

t = 3l + 6l = 3t − 6

B l + t = 108Dl + t = 108

t = 3l − 6l = 3t + 6

  1. Cristina’s Cleaners charges a $50 initial fee plus $10 for every half hour of labor for their cleaning service. Martin’s Maid service has no initial fee, but charges $35 per hour of labor. Write a system of equations representing the charges by both cleaning companies.
  1. Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 108 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?

A l + t = 108C l + t = 108

t = 3l + 6l = 3t − 6

B l + t = 108Dl + t = 108

t = 3l − 6l = 3t + 6

  1. Cristina’s Cleaners charges a $50 initial fee plus $10 for every half hour of labor for their cleaning service. Martin’s Maid service has no initial fee, but charges $35 per hour of labor. Write a system of equations representing the charges by both cleaning companies.