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Middle SchoolMathematics 5+3 pts


Créstòr bought a terrarium that is 24 inches wide, 48 inches long and 20 inches high. A bag of special dirt at the pet store only fills 1,000 cubic inches and costs $8.00 per bag.

Part A: How many bags does Crèstòr need to fill his terrarium?
Part B: How much do the bags cost after a 6% sales tax?

Answer 1

Answer:

Part A: 23 bags

Part B: $195.04

Step-by-step explanation:

Part A

Since the terrarium is rectangular prism, we are using the formula for the volume of a prism to find its volume:

$V=wlh$

Where

$V$ is the volume of the prism (terrarium)

$w$ is the width of the prism (terrarium)

$l$ is the length of the prism (terrarium)

$h$ is the height of the prism (terrarium)

We know from our problem that the terrarium is 24 inches wide, 48 inches long and 20 inches high, so $w=24cm$, $l=48cm$, and $h=20cm$. Replacing values:

$V=wlh$

$V=(24in)(48in)(20in)$

$V=23040in^{3}$

We know that each bag fills 1,000 cubic inches, so, to find how many bags he needs to fill his terrarium, we should divide the volume of his terrarium by the volume of 1 bag:

Number of bags = $\frac{23040in^{3}}{1000in^{3}}$

Number of bags = 23.04 bags

which rounds to 23 bags

We can conclude that Crestor needs 23 bags to fill his terrarium.

Part B

First we need to find the total cost of the bags. We know from part A that Crestor needs 23 bags; we also know that each bag cost $8.00, so

Total cost = $8.00*23

Total cost = $184.00

Now, to find the total cost after a 6% sales tax, we need to add the 6% of $184,00 to the total cost:

Cost after sale tax = $184.00 + 6%($184.00)

To perform the multiplication we need to convert 6% to decimal. To do it, we need to divide it by 100%

Cost after sale tax = $184.00+\frac{6}{100} (184.00)$

Cost after sale tax = $16.00+0.06(184.00)$

Cost after sale tax = $184.00 + $11.04

Cost after sale tax = $195.04

We can conclude that the cost after sales tax is $195.04