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PROBLEM SET 1: Evaluating Algebraic Expressions

Instructions: Define a variable and write an algebraic expression for each problem. Evaluate the expression for the given values.

1. The charge for ice skating is [tex]$3 for the skate rental and $[/tex]2 per hour to skate. How much will you pay if you skate for:

Let [tex]\( h \)[/tex] be the number of hours you skate.

Expression: [tex]\( 3 + 2h \)[/tex]

If you skate for [tex]\( h \)[/tex] hours, the total cost is [tex]\( 3 + 2h \)[/tex].

2. A birthday party at the skating rink costs [tex]$60 to reserve a party area and $[/tex]2.50 per guest for skating and skate rental. How much will a party cost if you invite:

Let [tex]\( g \)[/tex] be the number of guests.

Expression: [tex]\( 60 + 2.50g \)[/tex]

(a) If you invite 8 guests, the total cost is [tex]\( 60 + 2.50 \times 8 \)[/tex].



Answer :

GinnyAnswer
Sure, let's solve this problem step by step.

First, let's define the necessary variables and expressions before evaluating them.

Variables and Expression:

- The fixed cost for reserving the party area is [tex]$60. - The cost per guest for skating and skate rental is $[/tex]2.50.
- The number of guests is given as 8.

Now, we can write an algebraic expression for the total cost of the birthday party:

[tex]\[ \text{Total Cost} = \text{Reservation Cost} + (\text{Cost per Guest} \times \text{Number of Guests}) \][/tex]

Plugging in the values:

- Reservation Cost = [tex]\( 60 \)[/tex] dollars
- Cost per Guest = [tex]\( 2.50 \)[/tex] dollars
- Number of Guests = [tex]\( 8 \)[/tex]

Substituting these values into the expression gives:

[tex]\[ \text{Total Cost} = 60 + (2.50 \times 8) \][/tex]

Next, we calculate the total cost:

1. First, multiply the cost per guest by the number of guests:
[tex]\[ 2.50 \times 8 = 20 \][/tex]

2. Then, add this amount to the reservation cost:
[tex]\[ 60 + 20 = 80 \][/tex]

Result:

The total cost of the party if you invite 8 guests is [tex]\( 80 \)[/tex] dollars.

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