Question

12. Jeremy got quote from iVan to move him into his new home. One quote was for a weekday move which is

for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890. The other quote was for a

weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515. If

iVan has set hourly rates for loading/unloading and packing/unpacking, what are these hourly rates?

Answer 1

Loading/unloading hourly rate: $70

Packing/unpacking hourly rate: $55

Explanation:

We can write this as a system of linear equations.

We define L as the loading/unloading hourly rate, and P as the packing/unpacking hourly rate.

"One quote was for a weekday move which is for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890":

`8L+6P=890`

"The other quote was for a weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515":

`5L+3P=515`

If we express L in function of P in the first equation, and then replace this value in the second equation, we have:

`8L+6P=890\\\\8L=890-6P\\\\L=(890-6P)/(8)`

`5L+3P=515\\\\5\cdot (890-6P)/(8)+3P=515\\\\556.25-3.75P+3P=515\\\\-0.75P=515-556.25=-41.25\\\\P=41.25/0.75=55`

Then, L is:

`L=(890-6P)/(8)=(890-6(55))/(8)=(890-330)/(8)=(560)/(8)=70`