How do you define a variable and write an expression for each phrase: the number of gallons in 21 quarts?

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Answer 1 · 2017-07-22T13:02:24

#5 1/4# gallons

The way to remember this relationship is to make a mental link between the word 'quart' and the word 'quarter'.

A quarter is #1/4# and there are 4 quarts in 1 gallon.

One way to do the conversion is to consider it as a ratio. So we can write:

Let the unknown count of gallons be #x#

#("count of gallons")/("count of quarts")->1/4=x/21#

Multiply both sides by #color(red)(21)#

#color(green)(1/4=x xx1/21" "->" "1/4color(red)(xx21)=x xx1/21color(red)(xx21))#

#" "color(green)((1color(red)(xx21))/4=x xx(color(red)(21))/21)#

But #21/21=1#

#" " 21/4 = x xx1#

#x=5 1/4# gallons