Respuesta :
Answer:
60 small boxes and 65 large boxes
Step-by-step explanation:
From the given information we can make two equations:
L + S = 125
60L + 30S = 5700
S represents the number of small boxes and L represents the number of large boxes.
To solve an equation we need there to be only one variable, so I solved for s in the first equation.
L + S = 125
S = 125 - L
Now I can plug this into the second equation
60L + 30S = 5700
60L + 30(125 - L) = 5700 (substitute S)
60L + 3750 - 30L = 5700
30L + 3750 = 5700 (combine like terms)
30L = 1950 (subtract 3750 from both sides)
L = 65 (divide both sides by 30)
Now that we know there are 65 larger boxes, plug in 65 for L to find S.
S = 125 - L
S = 125 - 65
S = 60
So there are 65 large boxes and 60 small boxes
Answer:
There are 65 60-lb boxes and 60 30-lb boxes.
Step-by-step explanation:
Method:
Define two variables for the two unknowns. Set up a system of two equations in two variables. One equation deals with the numbers of boxes. The other equation deals with the weights. Solve the system of equations.
Define variables:
Let x = number of 60-lb boxes.
Let y = number of 30-lb boxes.
Equation dealing with numbers of boxes:
The total number of boxes is x + y. We are told the total number of boxes is 125, so the first equation is:
x + y = 125
Equation dealing with weights:
x number of 60-lb boxes weight 60x.
y number of 30-lb boxes weight 30y.
The total weight of all boxes is 60x + 30y. We are told the total weight is 5700 lb. The second equation is:
60x + 30y = 5700
System of two equations in two variables:
x + y = 125
60x + 30y = 5700
Solution of the system of equations by the substitution method:
Solve the first equation for x:
x + y = 125
Subtract y from both sides.
x = 125 - y
Substitute 125 - y for x in the second original equation.
60x + 30y = 5700
60(125 - y) + 30y = 5700
Distribute the 60.
7500 - 60y + 30y = 5700
Combine y-terms on left side.
7500 - 30y = 5700
Subtract 7500 from both sides.
-30y = -1800
Divide both sides by -30.
y = 60
There are 60 30-lb boxes.
Now substitute 60 for y in the first original equation and solve for x.
x + y = 125
x + 60 = 125
Subtract 60 from both sides.
x = 65
There are 65 60-lb boxes.
Answer: There are 65 60-lb boxes and 60 30-lb boxes.
Check:
The given information is there there are 125 boxes, and the total weight is 5700 lb.
The total number of boxes is 65 boxes + 60 boxes = 125 boxes. This checks with the given information.
The total weight is
65 * 60 lb + 60 * 30 lb = 3900 lb + 1800 lb = 5700 lb
This checks with the given information.
Our solution is correct.