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

By setting up an equation using the average weight formula and solving for x, we find that x equals 5. Subsequently, the heavier carton weighs 13 pounds, and the lighter carton weighs 7 pounds, making the heavier carton weigh 6 pounds more than the lighter carton.

Step-by-step explanation:

The question involves finding out how many more pounds the heavier carton weighs compared to the lighter carton when given their weights in terms of x and the average weight.

Firstly, we are given that the weights of the two cartons are 3x - 2 and 2x - 3 pounds, and their average weight is 10 pounds.

To find the value of x, we need to set up an equation using the average weight formula, which is:

(Weight of Carton 1 + Weight of Carton 2) / 2 = Average Weight

Substituting the given weights and average weight into the formula, we get:

((3x - 2) + (2x - 3)) / 2 = 10

Solving the equation by combining like terms and multiplying both sides by 2 to eliminate the fraction gives:

5x - 5 = 20

Adding 5 to both sides and then dividing by 5:

x = 5

Now, let's find the actual weight of each carton:

Weight of the first carton = 3x - 2 = 3(5) - 2 = 13 pounds

Weight of the second carton = 2x - 3 = 2(5) - 3 = 7 pounds

Lastly, we determine how many more pounds the heavier carton weighs compared to the lighter one:

13 pounds - 7 pounds = 6 pounds

Therefore, the heavier carton weighs 6 pounds more than the lighter carton.

Answer 2

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\\\\(5(x-1))/(2)=10`

Now multiplying both side by
`(2)/(5)` we get;

`(5(x-1))/(2)*(2)/(5)=10* (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*5-2=15-2 =13\ pounds`

Weigh of Carton 2 =
`2x-3=2*5-3=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.