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valentinak56 [21]
2 years ago
14

Mrs. Bhatia's closet consists of two sections, each shaped like a rectangular prism. She plans to buy mothballs to keep the moth

s away. She needs one box for every 32 cubic feet of space. How many boxes should she buy?
Mathematics
1 answer:
AveGali [126]2 years ago
7 0

Answer:

6.5 boxes

Step-by-step explanation:

Given

See attachment for closet

Required

Determine the number of boxes needed to fill the closet

First, we calculate the volume of the two section.

According to the attachment

The first section has the following dimension:

Width = 5ft

Length = 4ft

Height = 8ft

The second has the following dimension:

Width = 3ft ---- see the last label at the top

Length = 2ft --- This is calculated by subtracting the length of the first section (4ft) from the total length of the closet (6ft) i.e. 6ft - 4ft

Height = 8ft

So: The volume of the closet is:

Volume = W_1 * L_1 * H_1 + W_2 * L_2 * H_2

Volume = 5ft * 4ft * 8ft + 3ft * 2ft * 8ft

Volume = 160ft^3 + 48ft^3

Volume = 208ft^3

The number of box needed is then calculated by dividing the volume of the closet (208ft^3) by the volume of each box (32ft^3)

Boxes = \frac{208ft^3}{32ft^3}

Boxes= \frac{208}{32}

Boxes = 6.5

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ryzh [129]
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let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

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\bf \begin{array}{lccclll}
&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\
&------&------&------\\
\textit{25\% syrup}&10&0.25&2.5\\
\textit{pur water}&x&0.00&0.00x\\
------&------&------&------\\
\textit{10\% mixture}&y&0.10&0.10y
\end{array}
\\\\\\
\begin{cases}
10+x=\boxed{y}\\
2.5+0.00x=0.10y\\
----------\\
2.5 = 0.10\left( \boxed{10+x} \right)
\end{cases}
\\\\\\
2.5=1 + 0.10x\implies 1.5=0.10x
\\\\\\
\cfrac{1.5}{0.10}=x\implies 15=x
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Choose 1 to substitute in for x to find the ordered pair.

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