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?

1 Answer
Nov 11, 2017

Answer:

26 reals had the same value as #3 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

#color(blue)("Ratio format type 1")#

Initial condition: # "pesos: reals " ->color(green)( 1:8)" "........Condition(1)#

Target condition #"pesos: reals "-> x:26" ".....Condition(2)#

So we need to change the 8 in #Condition(1)# into 26

Note that if we multiply the 8 by #color(red)(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)])#

#color(white)("")"pesos: reals "->color(white)("d") [color(white)(2/2)3 1/4color(white)(2/2)]:[color(white)(2/2)26color(white)(2/2)]#
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#color(blue)("Ratio format type 2")#

#ul("Format")# as that of a fraction ( IS NOT A FRACTION OF THE WHOLE)

#("pesos")/("reals") -> 1/8#

As before we use #color(red)(26/8)#

#color(green)( ("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")( 3 1/4) /26)#

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26 reals had the same value as #3 1/4# pesos