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
no
your wrong
How is he wrong?
Let's start by setting up appropriate variables to represent the weights of Ling, her suitcase, and her knapsack.
Let L be the weight of Ling.
Let S be the weight of her suitcase.
Let K be the weight of her knapsack.
According to the given information, we have three pieces of information:
1. "Ling is three times as heavy as her packed suitcase":
This can be written as L = 3S.
2. "Her suitcase is 20 pounds heavier than her knapsack":
This can be written as S = K + 20.
3. "The weights of Ling, her suitcase, and her knapsack total 170 pounds":
This can be written as L + S + K = 170.
Now we have a system of two equations with three variables:
Equation 1: L = 3S
Equation 2: S = K + 20
Equation 3: L + S + K = 170
To solve this system, we can use substitution. Let's substitute L in terms of S from Equation 1 into Equation 3:
(3S) + S + K = 170
Simplifying this equation, we get:
4S + K = 170 (Equation 4)
Now we have two equations:
Equation 2: S = K + 20
Equation 4: 4S + K = 170
Substituting Equation 2 into Equation 4:
4(K + 20) + K = 170
Expanding and rearranging terms:
4K + 80 + K = 170
5K + 80 = 170
5K = 170 - 80
5K = 90
K = 90/5
K = 18
Now that we know the weight of the knapsack is 18 pounds, we can substitute this value back into Equation 2 to find the weight of the suitcase (S):
S = 18 + 20
S = 38
Finally, substituting the values of S and K into Equation 1, we can find the weight of Ling (L):
L = 3S
L = 3(38)
L = 114
Therefore, Ling weighs 114 pounds, her suitcase weighs 38 pounds, and her knapsack weighs 18 pounds.
If Ling, suitcase, and backpack weigh x,y,z, respectively, then we have
x = 3y
y = z+20
x+y+z = 170
so,
3y + y + y-20 = 170
5y = 190
y = 38
So,
Ling weighs 114
suitcase: 38
backpack: 18