Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and he earns money each Saturday morning at his grandmother’s store. Write an inequality for the amount of money Carlos will need to earn each Saturday morning, and describe the solutions. Assume Carlos will earn the same amount each Saturday morning.(2 points)
x+
≥
, where x is the amount Carlos earns each Saturday morning. Carlos must earn at least $
each Saturday morning to have at least $200 in four weeks.
30 + 4x ≥ 200
Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and he earns money each Saturday morning at his grandmother’s store. Write an inequality for the amount of money Carlos will need to earn each Saturday morning, and describe the solutions. Assume Carlos will earn the same amount each Saturday morning.(2 points)
x+
≥
, where x
is the amount Carlos earns each Saturday morning. Carlos must earn at least $
each Saturday morning to have at least $200 in four weeks.
The inequality is x ≥ (200 - 30) / 4.
The solutions to this inequality represent the minimum amount of money Carlos will need to earn each Saturday morning to have at least $200 in four weeks.
The inequality that represents the amount of money Carlos will need to earn each Saturday morning is: x ≥ (200 - 30)/4.
To understand how we arrived at this inequality, let's break it down step by step:
1. First, we need to determine how much money Carlos needs to save in four weeks. He wants to save at least $200.
2. Carlos's mom gives him $30 as a starting point. So, to reach his goal of $200, he needs to earn an additional $200 - $30 = $170 in four weeks.
3. Since he earns money each Saturday morning, we need to divide the remaining amount of money, $170, by the number of Saturdays in four weeks, which is 4. This gives us $170/4 = $42.50.
4. However, we need to round up to ensure Carlos earns an amount each Saturday morning that will guarantee he saves at least $200. Therefore, we round up $42.50 to the nearest whole number, which is $43.
5. Finally, the inequality that represents the amount of money Carlos will need to earn each Saturday morning is x ≥ $43, where x is the amount Carlos earns each Saturday morning.
The solutions to this inequality are any values of x that are greater than or equal to $43. Carlos must earn at least $43 each Saturday morning in order to have at least $200 in four weeks.