# In the 16th century, Spain had a silver coin called a peso. The coin was divided into 8 reals. Reals were stamped with an 8, and became known as pieces of eight. How many pesos would have been equivalent to 26 pieces of eight?

Nov 11, 2017

26 reals had the same value as $3 \frac{1}{4}$ pesos

#### Explanation:

Let the unknown count of 'peso' coins be $x$

You have more reals than pesos

Using two format types of ratio

$\textcolor{b l u e}{\text{Ratio format type 1}}$

Initial condition: $\text{pesos: reals " ->color(green)( 1:8)" } \ldots \ldots . . C o n \mathrm{di} t i o n \left(1\right)$

Target condition $\text{pesos: reals "-> x:26" } \ldots . . C o n \mathrm{di} t i o n \left(2\right)$

So we need to change the 8 in $C o n \mathrm{di} t i o n \left(1\right)$ into 26

Note that if we multiply the 8 by $\textcolor{red}{\frac{26}{8}}$ we get the value we need.

In ratio; for multiply or divide, what you do to one value you also do to the other.

color(white)("d")color(green)( [1] : [8]color(white)("d")color(white)("ddd")->color(white)("d")[1color(red)(xx26/8)]:[8color(red)(xx26/8)])

$\textcolor{w h i t e}{\text{)"pesos: reals "->color(white)("d}} \left[\textcolor{w h i t e}{\frac{2}{2}} 3 \frac{1}{4} \textcolor{w h i t e}{\frac{2}{2}}\right] : \left[\textcolor{w h i t e}{\frac{2}{2}} 26 \textcolor{w h i t e}{\frac{2}{2}}\right]$
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$\textcolor{b l u e}{\text{Ratio format type 2}}$

$\underline{\text{Format}}$ as that of a fraction ( IS NOT A FRACTION OF THE WHOLE)

$\left(\text{pesos")/("reals}\right) \to \frac{1}{8}$

As before we use $\textcolor{red}{\frac{26}{8}}$

$\textcolor{g r e e n}{\left(\text{pesos")/("reals")color(white)("d") ->color(white)("d") 1/8 color(white)("d")->color(white)("d")(1color(red)(xx26/8))/(8color(red)(xx26/8))color(white)("d") ->color(white)("d}\right) \frac{3 \frac{1}{4}}{26}}$

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26 reals had the same value as $3 \frac{1}{4}$ pesos