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Answer :
To solve this problem about the beverage sales at the store on Saturday, let's break it down into a system of linear equations.
We know the following:
1. The cost of a cold beverage ([tex]$c$[/tex]) is [tex]$1.50.
2. The cost of a hot beverage ($[/tex]h[tex]$) is $[/tex]2.00.
3. The total receipts from drinks on that day were [tex]$360.
4. The store sold four times as many cold beverages as hot beverages.
Based on this information, we can form our system of equations:
1. Equation for the number of beverages sold: Since 4 times as many cold beverages were sold as hot ones, we have:
\[
c = 4h
\]
This equation expresses the relationship between the quantities sold of cold and hot beverages.
2. Equation for the total revenue: The total sales brought in $[/tex]360, which includes the sales from both cold and hot beverages. The sales for each can be given by the number of drinks sold times their respective costs:
[tex]\[
1.5c + 2h = 360
\][/tex]
This equation accounts for all the sales by summing the revenue from cold beverages ([tex]$1.5c$[/tex]) and hot beverages ([tex]$2h$[/tex]) to equal the total receipts ($360).
These equations together form a system that represents the situation described:
- The equation [tex]\(c = 4h\)[/tex] represents the relationship between the number of cold and hot beverages sold.
- The equation [tex]\(1.5c + 2h = 360\)[/tex] represents the total sales for the beverages.
Thus, the correct system of linear equations to represent the beverage sales on Saturday is:
[tex]\[
c = 4h
\][/tex]
[tex]\[
1.5c + 2h = 360
\][/tex]
We know the following:
1. The cost of a cold beverage ([tex]$c$[/tex]) is [tex]$1.50.
2. The cost of a hot beverage ($[/tex]h[tex]$) is $[/tex]2.00.
3. The total receipts from drinks on that day were [tex]$360.
4. The store sold four times as many cold beverages as hot beverages.
Based on this information, we can form our system of equations:
1. Equation for the number of beverages sold: Since 4 times as many cold beverages were sold as hot ones, we have:
\[
c = 4h
\]
This equation expresses the relationship between the quantities sold of cold and hot beverages.
2. Equation for the total revenue: The total sales brought in $[/tex]360, which includes the sales from both cold and hot beverages. The sales for each can be given by the number of drinks sold times their respective costs:
[tex]\[
1.5c + 2h = 360
\][/tex]
This equation accounts for all the sales by summing the revenue from cold beverages ([tex]$1.5c$[/tex]) and hot beverages ([tex]$2h$[/tex]) to equal the total receipts ($360).
These equations together form a system that represents the situation described:
- The equation [tex]\(c = 4h\)[/tex] represents the relationship between the number of cold and hot beverages sold.
- The equation [tex]\(1.5c + 2h = 360\)[/tex] represents the total sales for the beverages.
Thus, the correct system of linear equations to represent the beverage sales on Saturday is:
[tex]\[
c = 4h
\][/tex]
[tex]\[
1.5c + 2h = 360
\][/tex]
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