# Mangos for Sale

## Task

A store was selling 8 mangos for \$10 at the farmers market.

Keisha said,

“That means we can write the ratio 10 : 8, or \$1.25 per mango.”

Luis said,

“I thought we had to write the ratio the other way, 8 : 10, or 0.8 mangos per dollar."

Can we write different ratios for this situation? Explain why or why not.

## IM Commentary

The purpose of this task is to generate a classroom discussion about ratios and unit rates in context. Sometimes students think that when a problem involves ratios in a context, whatever quantity is written first should be the first quantity in the ratio a:b. However, because the context itself does not dictate the order, it is important to recognize that a given situation may be represented by more than one ratio. An example of this is any problem involving unit conversions; sometimes one wants 3 feet : 1 yard and the associated unit rate 3 feet per yard and sometimes one wants 1 yard : 3 feet and the associated unit rate $\frac13$ yard per foot.

A similar task that provides students an opportunity to choose between the two different ratios and associated unit rates based on their usefulness is in development.

## Solution

Yes, this context can be modeled by both of these ratios and their associated unit rates. The context itself doesn’t determine the order of the quantities in the ratio; we choose the order depending on what we want to know.

## Mangos for Sale

A store was selling 8 mangos for \$10 at the farmers market.

Keisha said,

“That means we can write the ratio 10 : 8, or \$1.25 per mango.”

Luis said,

“I thought we had to write the ratio the other way, 8 : 10, or 0.8 mangos per dollar."

Can we write different ratios for this situation? Explain why or why not.