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