Question

1. a delivery service charges a base fee of $5 plus $2.50 for each package delivered. if the total cost for delivering a certain number of packages is $25, determine how many packages were delivered.

x - #
y = total $

m = 2.50
b = 5
y = 2.50x + 5
25 = 2.50x + 5

1. a youth club is organizing a camping trip. the initial number of boys signed up is 40, and each week, 2 more boys join the trip. how long will it take for there to be 100 boys signed up?

x = # days
y = total boys

m = 2
b = 40
y = 2x + 40
100 = 2x + 40
30 = x

1. the sum of marias age and twice her sisters age is 36. write a linear equation to represent this relationship and determine marias age if her sister is 8 years old.

x = marias age
y = sisters age

x + 2y = 36
x + 2(8) = 36
x + 16 = 36
x = 20

1. a taxi service charges a fixed fee of $8 plus $1.75 for each mile traveled. if the total cost for a taxi ride is $25, determine the number of miles traveled.

Explanation:

Problem 1

Step1: Define linear cost equation

Let $x$ = number of packages, $y$ = total cost. The equation is $y = 2.50x + 5$.

Step2: Substitute total cost $y=25$

$25 = 2.50x + 5$

Step3: Solve for $x$

Subtract 5 from both sides: $25 - 5 = 2.50x$ $\implies$ $20 = 2.50x$
Divide by 2.50: $x = \frac{20}{2.50} = 8$

Problem 2

Step1: Define linear growth equation

Let $x$ = number of weeks, $y$ = total boys. The equation is $y = 2x + 40$.

Step2: Substitute total boys $y=100$

$100 = 2x + 40$

Step3: Solve for $x$

Subtract 40 from both sides: $100 - 40 = 2x$ $\implies$ $60 = 2x$
Divide by 2: $x = \frac{60}{2} = 30$

Problem 3

Step1: Write linear age equation

Let $x$ = Maria's age, $y$ = sister's age. The equation is $x + 2y = 36$.

Step2: Substitute sister's age $y=8$

$x + 2(8) = 36$ $\implies$ $x + 16 = 36$

Step3: Solve for $x$

Subtract 16 from both sides: $x = 36 - 16 = 20$

Problem 4

Step1: Define linear cost equation

Let $x$ = number of miles, $y$ = total cost. The equation is $y = 1.75x + 8$.

Step2: Substitute total cost $y=25$

$25 = 1.75x + 8$

Step3: Solve for $x$

Subtract 8 from both sides: $25 - 8 = 1.75x$ $\implies$ $17 = 1.75x$
Divide by 1.75: $x = \frac{17}{1.75} = \frac{68}{7} \approx 9.71$

Answer:

1. 8 packages
2. 30 weeks
3. Linear equation: $x + 2y = 36$; Maria's age: 20 years old
4. $\frac{68}{7}$ (or approximately 9.71) miles