Respuesta :
Answer:
heavier carton weights 6 pounds more than the lighter carton.
Step-by-step explanation:
Given:
Weigh of Carton 1 = [tex]3x-2 \ pounds[/tex]
Weigh of carton 2 = [tex]2x-3 \ pounds[/tex]
Average weight of cartons is = 10 pounds.
We need to find the heavier carton weights how many more pounds than the lighter carton.
Solution:
We know that;
Average weight of cartons is equal to sum of weighs of carton 1 and carton 2 and then divided by 2.
framing in equation form we get;
[tex]\frac{3x-2+2x-3}2=10\\\\\frac{5x-5}2=10\\\\\frac{5(x-1)}{2}=10[/tex]
Now multiplying both side by [tex]\frac{2}{5}[/tex] we get;
[tex]\frac{5(x-1)}{2}\times\frac{2}{5}=10\times \frac{2}{5}\\\\x-1= 4[/tex]
Adding both side by 1 we get;
[tex]x-1+1=4+1\\\\x=5[/tex]
Now weigh of Carton 1 = [tex]3x-2=3\times5-2=15-2 =13\ pounds[/tex]
Weigh of Carton 2 = [tex]2x-3=2\times5-3=10-3 =7\ pounds[/tex]
now we can say that heavier carton is carton 1 and lighter carton is Carton 2.
We need to find the difference between carton 1 and carton 2.
Difference = [tex]13-7 =6[/tex]
Hence heavier carton weights 6 pounds more than the lighter carton.
