Ling is three times as heavy as her packed suitcase. Her suitcase is 20 pounds heavier than her knapsack. The weights of Ling, her suitcase, and her knapsack total 170 pounds. How much does each weigh?
Identify a variable, set up an equation, and solve. Thanks so much
L = 3s
k = s -20
s + 3s + s-20 = 170
Solve for s, then k and L.
To solve this problem, let's set up a variable for the weight of Ling's knapsack.
Let's call the weight of Ling's knapsack "x" pounds.
According to the problem, Ling's suitcase is 20 pounds heavier than her knapsack. So, the weight of the suitcase would be x + 20 pounds.
Also, it is given that Ling is three times as heavy as her packed suitcase. This means her weight would be 3 times the weight of the suitcase, so Ling's weight would be 3(x + 20) pounds.
The total weight of Ling, her suitcase, and her knapsack is given as 170 pounds. Thus, the equation can be formed as:
x + (x + 20) + 3(x + 20) = 170
Now, let's solve this equation to find the value of "x" and then calculate the weights of Ling, her suitcase, and her knapsack.
Combining like terms:
x + x + 20 + 3x + 60 = 170
Simplifying the equation:
5x + 80 = 170
Subtracting 80 from both sides:
5x = 90
Dividing both sides by 5:
x = 18
Now that we have the value of "x", we can substitute it back into the other expressions to find the weights.
Weight of Ling's knapsack (x): 18 pounds
Weight of Ling's suitcase (x + 20): 18 + 20 = 38 pounds
Weight of Ling (3(x + 20)): 3(18 + 20) = 3(38) = 114 pounds
Therefore, Ling's knapsack weighs 18 pounds, her suitcase weighs 38 pounds, and Ling herself weighs 114 pounds.