Question

writing algebraic equations from word problems

1. fort bend gym charges a $50 joining fee to activate a membership and $25 each month. write an

equation for the total oost.
a. determine the slope and what it represents in the story.
b. determine the y - intercept and what it represents in the story.
c. write the equation:

1. an airplane 30,000 feet above the ground begins to descending at a rate of 2,000 feet per

minute. write an equation to represent the height of the airplane.

1. jaxon rented a taxi from fort bend taxi company. the taxi company charges a flat fee of $3.00

and $0.75 per mile. write an equation to represent the total cost.

1. a local restaurant charges a $3 fee delivery fee and $5 for each pizza purchased. write an

equation for the cost, y, after x number of pizzas are delivered to one home.

1. nancy drives 60 miles per hour on interstate 45. write an equation for the distance traveled, d,

after t number of hours driven.

1. curtis worked all summer and saved $1200. he plans to spend $15 per week on lunch. write an

equation for the total amount, y, he has after x weeks.

1. the width of a rectangle is 6cm more than the length. the perimeter of the rectangle is 52cm.

write an equation to find the length, l.

Explanation:

Step1: Analyze problem 1

Let \(x\) be the number of months. The total cost \(y\) has a fixed part (\(50\)) and a variable part (\(25x\)).

a. Slope

The slope \(m = 25\). It represents the cost per month.

b. Y - intercept

The \(y\)-intercept \(b = 50\). It represents the joining fee.

c. Equation

Using the slope - intercept form \(y=mx + b\), the equation is \(y = 25x+50\).

Step2: Analyze problem 2

Let \(x\) be the number of minutes. The initial height is \(30000\) and the rate of descent is \(2000\) (so slope \(m=- 2000\)). Using \(y = mx + b\), the equation for height \(y\) is \(y=-2000x + 30000\).

Step3: Analyze problem 3

Let \(x\) be the number of miles. The flat fee \(b = 3\) and cost per mile \(m = 0.75\). Using \(y=mx + b\), the equation is \(y=0.75x + 3\).

Step4: Analyze problem 4

Let \(x\) be the number of pizzas. Delivery fee \(b = 3\) and cost per pizza \(m = 5\). Using \(y=mx + b\), the equation is \(y = 5x+3\).

Step5: Analyze problem 5

Using the formula \(d=rt\) (where \(r\) is rate and \(t\) is time). Here \(r = 60\), so the equation is \(d = 60t\).

Step6: Analyze problem 6

Let \(x\) be the number of weeks. Initial amount \(b = 1200\) and amount spent per week \(m=-15\). Using \(y=mx + b\), the equation is \(y=-15x + 1200\).

Step7: Analyze problem 7

Let the length be \(l\). Then the width \(w=l + 6\). The perimeter formula \(P=2(l + w)\). Substituting \(w=l + 6\) and \(P = 52\), we get \(52=2(l+(l + 6))\).

Answer:

1.

• a. Slope \(m = 25\) (cost per month)
• b. \(y\)-intercept \(b = 50\) (joining fee)
• c. \(y = 25x+50\)

1. \(y=-2000x + 30000\)
2. \(y=0.75x + 3\)
3. \(y = 5x+3\)
4. \(d = 60t\)
5. \(y=-15x + 1200\)
6. \(52=2(l+(l + 6))\)