Linear and System of Equations Word Problems Lesson & Notes

​Linear and System of Equations Word Problems Lesson & Notes

​Warm-Up

By NANCY HEAGERTY

Fill in the Blanks

Solve the system of equations.

$3x-2y=7$

$y=\frac{3}{2}x+5$

Multiple Select

Select three expression that are equivalent to -

$$6x^2-12x-18$$

• $$3\left(2x^2-4x-6\right)$$

• $$\left(6x+1\right)\left(x-18\right)$$

• $$3\left(2x+6\right)\left(x-1\right)$$

• $$6\left(x^2-2x-3\right)$$

• $$6\left(x+1\right)\left(x-3\right)$$

​Lesson

​Linear Word Problems

​This is the slope intercept form. The m represents the slope or rate of change. The b represents the y-intercept or what will always remain the same. The x represents what is changing and the y represents what you arec finding.

​Example 1:

​Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 feet per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?

​Example 2:

​For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation  for the cost, C, after h hours of babysitting. What do you think the slope and the y intercept represent? How much money will she make if she baby-sits 5 hours?  

Open Ended

A plumber charges $25 for a service call plus $50 per hour of service. Write an  equation in slope-intercept form for the cost, C, after h hours of service. What will be  the total cost for 8 hours of work? 10 hours of work?

Open Ended

 Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an  additional 25 pounds each week. Write and graph the equation for the total pounds, P, of aluminum cans after w weeks. What does the slope and y-intercept represent? How  long will it take Rufus to collect 400 pounds of cans?  

Open Ended

 A canoe rental service charges a $20 transportation fee and $30 dollars an hour to  rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe  for x hours. What is the cost of renting the canoe for 6 hours?

​System Word Problems

​Example 3:

​Seth’s father is thinking of buying his son a six-month movie pass for $40. With the  pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must  Seth attend in order for it to benefit his father to buy the pass?  

​Example 4:

The sum of two consecutive numbers is 123. Find the numbers.

​Example 5:

The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.

Open Ended

The sum of two numbers is 36. Twice the first number minus the second is 6.

Find the numbers.

Open Ended

The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $13.25. Two boxes of envelopes and 6 boxes of notebook paper cost $17. Find the cost of each.

Open Ended

The sum of two consecutive numbers is 85. Find the numbers.

Open Ended

Find two consecutive even numbers whose sum is 54.

Open Ended

A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower cost $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold.