Section Introduction on Connecting English with Math & Graphing Lines
Converting Word into Algebra for the basic Operations
example 1: Convert the following into algebra to expressions:
- "+": 4 more than a number
- "-": 4 less than a number
- "
\times": Three "times" a number - "of": Three of a number OR half of a number
Converting Words into Algebra Equation
A first example with percentage
example: 60\% of the school population is 300. What is the 100\% of the population?
Solution:
500 is the population of the school.
Converting words into Equations
example: Find a number when subtracted by 4 it's the same as when the number has been increased by 3 and then halved.
n = 11
How about division?
Typically here is what we do when we talk about division:
- dividend รท divisor = quotient
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.
(b) Isolate the variable for the number of jellybeans in your equation.
(c) If Jim bought 250 g of Pike, how many grams of Blonde did he buy?
(d) If Jim bought 150 g Blonde, how many grams of Pike did he buy?
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.
ex Two consecutive numbers add up to 55. What are the two numbers?
Graphing Lines
y = mx + b form
Ax + By = C
Intersection of Lines
example: Find the intersection point between the two lines below.
\displaystyle y = \frac{1}{2}x -1\displaystyle y = -\frac{3}{4}x + 6
The two lines share the point of intersection say (a, b).
Since (a, b) is on both lines they can be now written in terms of a and b in the following way.
\displaystyle b = \frac{1}{2}a -1\displaystyle b = -\frac{3}{4}a + 6
Therefore,
\displaystyle
\left(\frac{28}{5}, \frac{9}{5}\right)