Question

five dvds are packaged in plastic wrap. five packages are packed in a box. five boxes are packed in a crate. how many dvds are packed in a crate? represent the number of dvds in a crate as a power.

Answer 1

The question is an illustration of proportion and exponents

The number of dvd is one crate is: $\mathbf{5^3\ dvds}$

From the question, the given parameters are:

$\mathbf{5\ dvd = 1\ wrap}$ ---- 5 dvds in 1 package

$\mathbf{5\ package = 1\ box}$ --- 5 packages in 1 box

$\mathbf{5\ boxes = 1\ crate}$ --- 5 boxes in 1 crate

The number of dvds in 1 crate is calculated as follows:

$\mathbf{5\ boxes = 1\ crate}$

Substitute 5 packages for 1 box in the above equation

$\mathbf{5 \times 5\ packages = 1\ crate}$

Substitute 5 dvds for 1 package in the above equation

$\mathbf{5 \times 5 \times 5\ dvd= 1\ crate}$

Apply law of indices

$\mathbf{5^{1 + 1 + 1}\ dvd= 1\ crate}$

Express properly as:

$\mathbf{5^3\ dvd= 1\ crate}$

Rewrite as:

$\mathbf{1\ crate = 5^3\ dvd}$

Hence, the number of dvd is one crate is: $\mathbf{5^3\ dvds}$

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