College

1)

a) Toshi cuts 5 equal lengths from 100 cm of ribbon. Each length is [tex]y[/tex] cm.

Write the rule for the length of ribbon he has left.

b) How much ribbon is left if [tex]y = 12[/tex] cm?

There is [tex]\square[/tex] cm of ribbon left.

Answer :

Sure! Let's solve the question step-by-step.

1) a) Rule:

Toshi starts with a total of 100 cm of ribbon. He cuts the ribbon into 5 equal lengths, and each length is [tex]\( y \)[/tex] cm.

To find out how much ribbon is left after making these cuts, we can use the following formula:

[tex]\[ \text{Ribbon left} = \text{Total ribbon} - (\text{Number of pieces} \times \text{Length of each piece}) \][/tex]

So, the rule for the length of ribbon that Toshi has left is:

[tex]\[ \text{Ribbon left} = 100 - 5 \times y \][/tex]

This formula gives us the length of ribbon left after cutting the 5 pieces, each of length [tex]\( y \)[/tex].

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1) b) How much ribbon is left if [tex]\( y = 12 \, \text{cm} \)[/tex]?

We need to substitute [tex]\( y = 12 \, \text{cm} \)[/tex] into the rule we derived.

[tex]\[ \text{Ribbon left} = 100 - 5 \times 12 \][/tex]

First, calculate the total length of the pieces cut off:

[tex]\[ 5 \times 12 = 60 \][/tex]

Now, subtract that from the initial length of the ribbon:

[tex]\[ 100 - 60 = 40 \][/tex]

Therefore, there are [tex]\( 40 \, \text{cm} \)[/tex] of ribbon left.