Question

Generate a ratio table with at least two ratios equivalent to $10 per 15 tickets. Then describe how the table shows an additive structure and multiplicative structure.

Answer 1

Ratios are used to show proportions of related quantities.

The ratio table equivalent to $10 per 15 tickets is:

$\begin{array}{cc}{Amount}&{Tickets}&10&15&20&30&30&45&40&60\end{array}$

Given that:

Ratio = $10 per 15 tickets

Using proper notation, we have:

$Ratio = 10:15$

To generate a ratio table, we simply multiply or divide each part of the ratio by the same unit.

For instance,

Multiply by 2

$Ratio = 20:30$

Divide the original ratio by 5

$Ratio = 2:3$

A possible ratio table is:

$\begin{array}{cc}{Amount}&{Tickets}&10&15&20&30&30&45&40&60\end{array}$

The additive structure

From the above table, we can see that as the amount (x) increases by 10 units, the number of tickets (y) increases by 15 units.

So, the additive structure of the above table is:

$(x,y) \to (x_i+10,y_i + 15)$

The multiplicative structure

The multiplicative structure simply implies that the amount (x) and the number of tickets (y) be multiplied by the same unit.

So, the multiplicative structure of the above table is:

$(x,y) \to n(x_i,y_i)$

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