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Answer :
Sure! Let's solve this problem step-by-step.
We're given the following information:
- Cold beverages cost \[tex]$1.50 each.
- Hot beverages cost \$[/tex]2.00 each.
- The total sales on Saturday were \[tex]$360.
- Four times as many cold beverages were sold as hot beverages.
We want to create a system of linear equations that represents this situation.
1. Define the Variables:
- Let \( c \) represent the number of cold beverages sold.
- Let \( h \) represent the number of hot beverages sold.
2. Set Up the Equations:
- Since the receipt total is \$[/tex]360 and this amount includes both cold and hot beverages, we can write:
[tex]\[
1.5c + 2h = 360
\][/tex]
This equation represents the total sales in dollars from cold and hot beverages.
- We know from the problem that four times as many cold beverages as hot beverages were sold, which translates to:
[tex]\[
c = 4h
\][/tex]
This equation expresses the relationship between the quantities of cold and hot beverages sold.
3. The System of Equations:
From the two setups above, the system of equations that models this scenario is:
- [tex]\( c = 4h \)[/tex]
- [tex]\( 1.5c + 2h = 360 \)[/tex]
These two equations together describe the beverage sales on Saturday based on the problem's conditions.
We're given the following information:
- Cold beverages cost \[tex]$1.50 each.
- Hot beverages cost \$[/tex]2.00 each.
- The total sales on Saturday were \[tex]$360.
- Four times as many cold beverages were sold as hot beverages.
We want to create a system of linear equations that represents this situation.
1. Define the Variables:
- Let \( c \) represent the number of cold beverages sold.
- Let \( h \) represent the number of hot beverages sold.
2. Set Up the Equations:
- Since the receipt total is \$[/tex]360 and this amount includes both cold and hot beverages, we can write:
[tex]\[
1.5c + 2h = 360
\][/tex]
This equation represents the total sales in dollars from cold and hot beverages.
- We know from the problem that four times as many cold beverages as hot beverages were sold, which translates to:
[tex]\[
c = 4h
\][/tex]
This equation expresses the relationship between the quantities of cold and hot beverages sold.
3. The System of Equations:
From the two setups above, the system of equations that models this scenario is:
- [tex]\( c = 4h \)[/tex]
- [tex]\( 1.5c + 2h = 360 \)[/tex]
These two equations together describe the beverage sales on Saturday based on the problem's conditions.
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