Question

word problems

1. kara and jasmine go to the splash - o - mania water park.

the entrance fee is $20.00. kara rents a locker for $1.50 per hour. jasmine rents a tube for $3.00 per hour.

a) write an expression that represents the cost for kara

b) write an expression that represents the cost for jasmine.

c) what is a simplified expression for the total cost for both kara and jasmine to stay at the water park together for any number of hours?

1. you are selling used video games for $10 and used books for $4. the expression $10x + 4y$ provides a general expression for the value of your sales.

a) what does the variable $x$ and $y$ represent?

b) how much money do you receive if you sell 6 video games and 11 books?

Explanation:

Step1: Define variable for hours

Let $h$ = number of hours at the park.

Step2: Kara's cost expression

Fixed fee + hourly locker cost:
$20 + 1.50h$

Step3: Jasmine's cost expression

Fixed fee + hourly tube cost:
$20 + 3.00h$

Step4: Total cost expression

Add Kara and Jasmine's costs:
$(20 + 1.50h) + (20 + 3.00h)$

Step5: Simplify total cost

Combine like terms:
$20+20 + 1.50h+3.00h = 40 + 4.50h$

Step6: Identify variables for sales

Match prices to variables:
$10x$ = video game sales, $4y$ = book sales

Step7: Calculate total sales

Substitute $x=6$, $y=11$ into $10x+4y$:
$10(6) + 4(11) = 60 + 44$

Answer:

1)
a) $20 + 1.50h$
b) $20 + 3.00h$
c) $40 + 4.50h$
2)
a) $x$ represents the number of used video games sold; $y$ represents the number of used books sold.
b) $\$104$