Section Introduction on Connecting English with Math & Graphing Lines
Converting Word into Algebra for the basic Operations
ex Convert the following into algebra to expressions:
- "+": 4 more than a number
\rightarrow x + 4, 4 + x - "-": 4 less than a number
\rightarrow x - 4 - "
\times": Three "times" a number\rightarrow 3x - "of": Three of a number (
3x) OR half of a number (\dfrac{1}{2}x)
Converting Words into Algebra Equation
A first example with percentage
ex 60\% of the school population is 300. What is the 100\% of the population?
Therefore, 500 is the population of the school.
Converting words into Equations
ex Find a number when subtracted by 4 it's the same as when the number has been increased by 3 and then halved.
Therefore, the number is 11.
Word into Division
Typically here is what we do when we talk about division:
- dividend รท divisor = quotient
ex The quotient of a number divided by 6 is 10 with a remainder of 4. What is the number?
Therefore, the number is 64.
ex 2 54 has x groups of 5 with a remainder of 4. What is value of x?
Therefore, x = 10.
Modelling Cost of items
Jim is looking to buy a mixture of two coffee beans in StarCoffee. There are two different types of roast: Pike and Blonde. Jim is going to spend a total of \$24 on coffee beans. The Pike roast cost \$8/kg and the Blonde roast cost \$6/kg.
(a) Write an equation to represent Jim's purchases.
Cost = 8x + 6y = 24
(b) Isolate the variable for the number of jellybeans in your equation.
x = \dfrac{12 - 3y}{4}
(c) If Jim bought 250 g of Pike, how many grams of Blonde did he buy?
If Jim bought 250 g of Pike, then he bought y = \dfrac{11}{3} grams of Blonde.
(d) If Jim bought 150 g Blonde, how many grams of Pike did he buy?
If Jim bought 150 g Blonde, then he bought 2.8875 grams of Pike.
Geometry Set Up Example
ex The length of a rectangle is 4 cm less than 3 times the width. The perimeter is 36 cm. Find the width and length.
Therefore, the width of the rectangle is 5.5 cm and the length of the rectangle is 12.5 cm.
Consecutive Numbers
ex Two consecutive numbers add up to 55. What are the two numbers?
Therefore, the two numbers are 27 and 28.
Graphing Lines
ex Graph y = 2x - 1.
ex 2 Graph -\frac{2}{3}x + 5
ex 3 Graph 3x + 2y = 5
Intersection of Lines
ex Find the intersection point between the two lines below.
Therefore, the point of intersection is (\dfrac{28}{5}, \dfrac{9}{5}).