To determine the difference in price between a small bag and a large bag based on the given situation, follow these steps:
1. Understanding the Equation:
The equation given is:
[tex]\[
4S + 10L = 156
\][/tex]
Here, [tex]\(S\)[/tex] represents the number of small bags and [tex]\(L\)[/tex] represents the number of large bags. The coefficients of [tex]\(S\)[/tex] and [tex]\(L\)[/tex] (which are 4 and 10, respectively) represent the prices of these bags in dollars.
2. Interpret Price Coefficients:
- The coefficient 4 in front of [tex]\(S\)[/tex] indicates that the price of one small bag is \[tex]$4.
- The coefficient 10 in front of \(L\) indicates that the price of one large bag is \$[/tex]10.
3. Calculate the Difference in Prices:
To find the difference in price between a small bag and a large bag, subtract the price of the small bag (4 dollars) from the price of the large bag (10 dollars):
[tex]\[
10 - 4 = 6
\][/tex]
4. Conclusion:
The difference in price between a small bag and a large bag is:
[tex]\[
\$6
\][/tex]
Therefore, the difference in price between a small bag and a large bag is [tex]\(\$6\)[/tex].
