To landscape her 70 ft-by-60 ft rectangular backyard, your aunt is planning first to put down a 4-in. layer of topsoil. She can buy bags of topsoil at $2.50 per 3-ft^3 bag, with free delivery. Or, she can buy bulk topsoil for $22.00/yd^3, plus a $20 delivery fee. Which option is less expensive? Explain.

Question

anonymous · Answer

total area= 70*60
1st option=> 70*60/3
2nd option=> 70*60/22 +20 convert yard firstly

phi · Answer

My first thought is figure out how many cubic feet of soil you need.
that means you should change the depth of 4 inches to 1/3 of a foot, and figure the volume of a rectangular prism.

highschoolmom2010 · Answer

V=bh
V=(70*60)*1/3
V=4200*1/3 
V=1400 ft^3 

i think

phi · Answer

yes.  Now figure out how much option A costs.

highschoolmom2010 · Answer

1400 ft^3*$2.50=3500$

phi · Answer

I think the bags contain 3 cu ft of top soil

highschoolmom2010 · Answer

1400/3=467
467*2.50=1167.5

phi · Answer

yes.

now option B.

I would change cubic yards into cubic feet  so we can get a dollars per cubic foot price
from $22 per cubic yard.

a yard is 3 feet.  a cubic yard is a 3 foot by 3 foot by 3 foot cube.
You need to find the volume of a cube with a side of 3 feet.

highschoolmom2010 · Answer

v=bh
v=9*3
V=27

phi · Answer

yes there are 27 ft^3 in 1 yd^3

so now you have $22 per 27 ft^3
how much does it cost for 1400 ft^3 ?
and then add in the $20 delivery charge.

phi · Answer

I would do
$$ \frac{$22}{27 \text{ ft}^3 } \cdot 1400 \text{ ft}^3 +$20$$

highschoolmom2010 · Answer

1160.74

phi · Answer

Now the final part.  Which option is less expensive?

highschoolmom2010 · Answer

2nd one