Question

the skating rink charges $100 to reserve the rink, and then $5 per person. write an expression to represent the cost for any number of people.
$n =$ the number of people
$100 + 5n$
cost to reserve rink price per person

1. maria has three more than twice as many pens as liz. write an expression to represent the number of pens maria has.
2. an amusement park charges $28 to enter and $0.35 per ticket for rides. write an expression to represent the total amount spent.
3. drew has a job doing yard work. he is paid $15 per hour and a $20 bonus when he completes a yard. write an equation to represent the amount of money he earned after completing one yard.
4. santo made 4 less than twice as many cupcakes as lynn. write an equation to represent the number of cupcakes that santo made.
5. tom earned $5 mowing the lawn on saturday. he earned more money on sunday. write an equation that shows the amount of money tom has earned.
6. describe a problem situation that can be solved using the equation $2c + 3 = 15$ where $c$ represents the cost of an item.

Explanation:

Step1: Define variable for Liz's pens

Let \( p = \text{number of pens Liz has} \)

Step2: Write Maria's pen count

Twice Liz's pens: \( 2p \); add 3: \( 2p + 3 \)

Step1: Define variable for ride tickets

Let \( t = \text{number of ride tickets} \)

Step2: Write total cost

Entry fee + ticket cost: \( 28 + 0.35t \)

Step1: Define variable for work hours

Let \( h = \text{hours spent on yard work} \)

Step2: Write total earnings

Hourly pay + bonus: \( 15h + 20 \)

Step1: Define variable for Lynn's cupcakes

Let \( c = \text{number of cupcakes Lynn made} \)

Step2: Write Santo's cupcake count

Twice Lynn's cupcakes: \( 2c \); subtract 4: \( 2c - 4 \)

Step1: Define variables for earnings

Let \( s = \text{Sunday earnings}, T = \text{total earnings} \)

Step2: Write total earnings equation

Saturday + Sunday earnings: \( T = 5 + s \), where \( s > 5 \)

Step1: Frame scenario for \( 2c + 3 = 15 \)

Set context: 2 items + $3 fee = $15 total

Step2: Write full problem situation

"Sarah buys 2 identical notebooks, plus a $3 pack of stickers. Her total cost is $15. What is the cost \( c \) of one notebook?"

Answer:

1. \( 2p + 3 \) (where \( p \) = number of pens Liz has)
2. \( 28 + 0.35t \) (where \( t \) = number of ride tickets)
3. \( 15h + 20 \) (where \( h \) = hours of yard work)
4. \( 2c - 4 \) (where \( c \) = number of cupcakes Lynn made)
5. \( T = 5 + s \) (where \( s \) = Sunday earnings, \( s > 5 \), \( T \) = total earnings)
6. Sarah buys 2 identical notebooks, plus a $3 pack of stickers. Her total cost is $15. What is the cost \( c \) of one notebook?