Question

Two cartons weigh 3x-2 and 2x-3 pounds, respectively. If the average weight of the cartons is 10 pounds, the heavier carton weights how many more pounds than the lighter carton

Answer 1

Answer:

heavier carton weights 6 pounds more than the lighter carton.

Step-by-step explanation:

Given:

Weigh of Carton 1 = $3x-2 \ pounds$

Weigh of carton 2 = $2x-3 \ pounds$

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;

$\frac{3x-2+2x-3}2=10\\\\\frac{5x-5}2=10\\\\\frac{5(x-1)}{2}=10$

Now multiplying both side by $\frac{2}{5}$ we get;

$\frac{5(x-1)}{2}\times\frac{2}{5}=10\times \frac{2}{5}\\\\x-1= 4$

Adding both side by 1 we get;

$x-1+1=4+1\\\\x=5$

Now weigh of Carton 1 = $3x-2=3\times5-2=15-2 =13\ pounds$

Weigh of Carton 2 = $2x-3=2\times5-3=10-3 =7\ pounds$

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 = $13-7 =6$

Hence heavier carton weights 6 pounds more than the lighter carton.