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Answer :
To solve the problem, we need to establish a system of linear equations based on the information given:
1. Cost and Total Revenue:
- Cold beverages cost \[tex]$1.50 each.
- Hot beverages cost \$[/tex]2.00 each.
- The total revenue from beverage sales on Saturday was \[tex]$360.
2. Relationship between Cold and Hot Beverages:
- We know that 4 times as many cold beverages were sold as hot beverages.
Let's define:
- \( c \) as the number of cold beverages sold.
- \( h \) as the number of hot beverages sold.
Step-by-step:
1. Translate the Relationship into an Equation:
- Since 4 times as many cold beverages (\( c \)) were sold compared to hot beverages (\( h \)), we can write:
\[
c = 4h
\]
2. Revenue Equation:
- The total revenue from selling both types of beverages is \$[/tex]360. The contribution to this revenue from cold beverages is [tex]\( 1.5c \)[/tex], and from hot beverages, it is [tex]\( 2h \)[/tex].
- Therefore, the revenue equation is:
[tex]\[
1.5c + 2h = 360
\][/tex]
3. Form the System of Equations:
- Using the two equations we have, the system of linear equations representing the beverage sales on Saturday is:
[tex]\[
c = 4h
\][/tex]
[tex]\[
1.5c + 2h = 360
\][/tex]
These equations together model the conditions given in the problem. This system of equations can be solved to find out exactly how many cold and hot beverages were sold, but in this case, we were primarily asked to create the system itself.
1. Cost and Total Revenue:
- Cold beverages cost \[tex]$1.50 each.
- Hot beverages cost \$[/tex]2.00 each.
- The total revenue from beverage sales on Saturday was \[tex]$360.
2. Relationship between Cold and Hot Beverages:
- We know that 4 times as many cold beverages were sold as hot beverages.
Let's define:
- \( c \) as the number of cold beverages sold.
- \( h \) as the number of hot beverages sold.
Step-by-step:
1. Translate the Relationship into an Equation:
- Since 4 times as many cold beverages (\( c \)) were sold compared to hot beverages (\( h \)), we can write:
\[
c = 4h
\]
2. Revenue Equation:
- The total revenue from selling both types of beverages is \$[/tex]360. The contribution to this revenue from cold beverages is [tex]\( 1.5c \)[/tex], and from hot beverages, it is [tex]\( 2h \)[/tex].
- Therefore, the revenue equation is:
[tex]\[
1.5c + 2h = 360
\][/tex]
3. Form the System of Equations:
- Using the two equations we have, the system of linear equations representing the beverage sales on Saturday is:
[tex]\[
c = 4h
\][/tex]
[tex]\[
1.5c + 2h = 360
\][/tex]
These equations together model the conditions given in the problem. This system of equations can be solved to find out exactly how many cold and hot beverages were sold, but in this case, we were primarily asked to create the system itself.
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