Inequality: 2(p+4.75)≤ 100 Answer: No more than $45.25
Practice makes perfect
To write an inequality to represent this scenario, we will express the given information algebraically. Once we have done that, we will be able to solve the inequality.
Writing the Inequality
Zachary cannot spend more than $ 100 buying games for his brothers. Since this is the maximum amount he can spend on the games, he can spend any amount of money less than or equal to this amount.
amount spent on games ≤ 100
To find the amount Zachary can spend buying games, let's first consider the cost of one game. If we call the price of one game p, and it costs $4.75 to ship each game, we can express the total cost of one game algebraically.
p+4.75
We know that Zachary has 2 brothers and that he is buying the same game for both of them. Therefore, the total amount spent on games will be 2 times the cost of one game, which we found above.
2(p+4.75)= amount spent on games
We can substitute this algebraic expression to form our inequality.
2(p+4.75) ≤ 100
Solving the Inequality
Solving inequalities is done in the same way as solving equations, using inverse operations to isolate the variable. Just remember to reverse the inequality symbol when multiplying or dividing the inequality by a negative number.
To solve this inequality, we will start by distributing the outside factor to each term inside the parentheses.
