Digging a rectangular prism for a pool. it is 42 ft × 29.5 ft × 8ft. the hauling truck holds 452.5 cubic feet away in a load . how many truckloads of dirt will have to be hauled away to finish the job?

The volume of the prism = 42 * 29.5 * 8

= 9912 ft^3

Number of truckloads  needed = 9912 / 452.5

=  21.90

So the answer is 22 truckloads.

Recall that the amount of dirt that the truck hauls away will equal the volume of the pool.

If the pool's dimensions are 42 ft x 29.5 ft x 8 ft

and Volume = base * width * height

we can denote the base as 42 ft, the width as 29.5 ft, and the height as 8 ft.

Pool volume = 42 * 29.5 * 8

Pool volume = 9,912 cubic ft

Therefore

Dirt volume = 9,912 cubic ft

Assume the hauling truck is at capacity with 425.5 cubic feet.

If we want to know how many truckloads will need to be taken away, and we know how the volume of the dirt that will need to be removed and how much a truck will hold, then we need to divide our total volume of dirt by the volume of dirt that one truck can carry.

Number of truckloads = 9,912 ÷ 425.5

Number of truckloads = 23.295

Because the truck will still have extra after his 23rd haul, it will still have to make one last haul away, despite not being full.

We can then round up 23.295 truckloads to 24 truckloads.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

there is no image or shapes attacted

step-by-step explanation: