Let's solve the problem step-by-step.
1. Understanding the Variables:
- [tex]\( G \)[/tex]: the number of liters of goat milk Wang Hao wants to buy.
- [tex]\( C \)[/tex]: the number of liters of cow's milk Wang Hao wants to buy.
2. Understanding the Costs:
- Each liter of goat milk costs \[tex]$2.40.
- Each liter of cow's milk costs \$[/tex]1.20.
- Therefore, if Wang Hao buys [tex]\( G \)[/tex] liters of goat milk, the total cost for goat milk will be [tex]\( 2.40G \)[/tex] dollars.
- Similarly, if he buys [tex]\( C \)[/tex] liters of cow's milk, the total cost for cow milk will be [tex]\( 1.20C \)[/tex] dollars.
3. Formulating the Total Cost:
- The total amount of money spent by Wang Hao on both types of milk is the sum of the costs of goat milk and cow's milk.
- Therefore, the total cost is [tex]\( 2.40G + 1.20C \)[/tex] dollars.
4. Formulating the Inequality:
- Wang Hao's budget is at most \[tex]$15, which means the total cost of dairy products should not exceed \$[/tex]15.
- Thus, we need to express this relationship as an inequality.
- The inequality representing the number of liters of goat milk [tex]\( G \)[/tex] and cow's milk [tex]\( C \)[/tex] Wang Hao can buy within his budget is:
[tex]\[
2.40G + 1.20C \leq 15
\][/tex]
Therefore, the inequality that represents the number of liters of goat milk [tex]\( G \)[/tex] and cow's milk [tex]\( C \)[/tex] Wang Hao can buy without exceeding his budget of \$15 is:
[tex]\[
2.40G + 1.20C \leq 15
\][/tex]
