Question

1. silvio works in a hair salon. he has 50 regular customers. his customer base is growing at a rate of three new customers per month.

a) write an equation to describe the total number of customers.
let m represent:
let c represent:
equation

b) how long will it be before silvio has 125 customers?

1. paula bought a parrot. the bird had a 10 word vocabulary, but paula has taught it 3 new words per week.

a) write an equation to represent the number of words the bird can speak
let w represent :
let v represent:
equation

b) determine how large a vocabulary the parrot could have after 1 year (or 52 weeks)

1. the cost of jack’s cell phone is $150 plus $30 per month.

a) write an equation that describes the cost of jack’s cell phone as the months pass.
let m represent
let c represent
equation:

1. complete the table of values to find the rate of change.

x	y	rate of change = 1^st differences
0	-2
1	1
2	4
3	7
4	10
5	13

Explanation:

Problem 7

Step1: Define variables

Let $m$ = number of months, $C$ = total customers.

Step2: Form linear equation

Initial customers + new customers per month × months:
$C = 50 + 3m$

Step3: Solve for $m$ when $C=125$

Substitute $C=125$:
$125 = 50 + 3m$
Subtract 50 from both sides:
$125 - 50 = 3m$
$75 = 3m$
Divide by 3:
$m = \frac{75}{3} = 25$

Step1: Define variables

Let $w$ = number of weeks, $V$ = total vocabulary.

Step2: Form linear equation

Initial words + new words per week × weeks:
$V = 10 + 3w$

Step3: Calculate $V$ when $w=52$

Substitute $w=52$:
$V = 10 + 3(52)$
$V = 10 + 156 = 166$

Step1: Define variables

Let $m$ = number of months, $C$ = total cost.

Step2: Form linear equation

Fixed cost + monthly cost × months:
$C = 150 + 30m$

Answer:

a) $C = 50 + 3m$
b) 25 months

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Problem 8