Zane received a quote to move his belongings to his new house. the estimate from the mover is $675 for 6 hours of packing and 5 hours of moving. zane thinks he can reduce his cost by doing some of the packing and moving himself. if he does, the cost will decrease to $425 for 4 hours of packing and 3 hours of moving. if the mover charges a set hourly rate for packing and another set hourly rate for moving, what are these hourly rates?

To solve this problem you must apply the proccedure shown below:
 1. You have that :
 -The estimate from the moving is $675 for 6 hours of packing and 5 hours of moving. 
 - The cost will decrease to $425 for 4 hours of packing and 3 hours of moving.

 x: rate for packing.
 y: rate for moving.

 6x+5y=675
 4x+3y=425

  2. When you solve the system of equations shown above, you obtain:

 x=50
 y=75

 Therefore, the answer is: $50 (Rate for packing) and $75 (Rate for moving).

The equation representing total food consumption in days can be given as:

where represents total food taken which is =250 pounds and represnts the number of days the food will last.

The food will last for days.

Step-by-step explanation:

Total pounds of food taken at the beginning =  250 pounds

Food consumed per day = 12 pounds

Let the total food at the beginning be = pounds

Let number of days the food will last be = days

Using unitary method to find the food consumed in days.

If in 1 day food consumed = 12 pounds

Then, in days food consumption = pounds

So,the equation representing total food consumption in days can be given as:

Total food taken =250 pounds

Plugging in in the equation:

Solving for  

Dividing both sides by 12.

Simplifying fractions.

Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.

∴ days.

Thus, the food will last for days.