Alicia weighs 60lbs less than her father. Their combined eights total 300lbs at most. What is the most Alicia could weigh?
Alicia -- x
Father --x+60
x + x+60 < 300
2x < 240
x < 120
Let's assume Alicia's father weighs F lbs. We know that Alicia weighs 60lbs less than her father, so her weight can be expressed as F - 60 lbs.
The combined weight of Alicia and her father is given as 300 lbs at most. Therefore, we can create an inequality to represent this:
(F - 60 lbs) + F ≤ 300 lbs.
Simplifying the inequality, we have:
2F - 60 lbs ≤ 300 lbs.
Adding 60 lbs to both sides, we get:
2F ≤ 360 lbs.
Dividing both sides by 2, we have:
F ≤ 180 lbs.
Since Alicia weighs 60 lbs less than her father, the most Alicia could weigh is F - 60 lbs, which is:
180 lbs - 60 lbs = 120 lbs.
Therefore, the most Alicia could weigh is 120 lbs.
To find the maximum weight Alicia could have, we need to make some assumptions. Let's assume that Alicia's father weighs the maximum amount possible while Alicia weighs the minimum amount possible.
Let's define A as Alicia's weight and F as her father's weight. We are given that Alicia weighs 60 pounds less than her father. So, we can set up the equation:
A = F - 60
We also know that their combined weight is at most 300 pounds. Thus, we can write another equation:
A + F ≤ 300
Now, let's substitute the first equation into the second equation:
(F - 60) + F ≤ 300
Simplifying this equation, we get:
2F - 60 ≤ 300
Add 60 to both sides:
2F ≤ 360
Divide by 2:
F ≤ 180
Since Alicia's father's weight cannot exceed 180 pounds, we can assume that he weighs 180 pounds. Now, let's substitute this value back into the first equation to find Alicia's weight:
A = F - 60 = 180 - 60 = 120
Therefore, the maximum weight Alicia could have is 120 pounds.