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Percentage calculations are quite common in everyday situations, such as figuring out discounts or sales prices. In this exercise, we are given that Yuki bought a dress at a sale price that was 60% of the original price.

To solve percentage problems, it's essential to convert the percentage into a decimal. For example, 60% becomes 0.60.

• You multiply the original price by this decimal to find the sale price.
• In this case, we set the equation as: \[ 0.60 \times P = 72 \]

Breaking down numbers into percentages makes it easier to manage and calculate. Remember, when dealing with percentages:

• Always convert them to decimals.
• Use multiplication to find part of a whole.
• Use division to find the total when given a part.

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Linear equations form the foundation of solving many algebraic problems, including this one. Setting up the right equation is key to finding the answer.

In this problem, we know that the sale price of the dress is 60% of the original price. We translate this into a linear equation:

First, identify the variables. Here, let \( P \) represent the original price. The equation is:

\[ 0.60 \times P = 72 \]

A linear equation typically has the format \( ax + b = c \) where \( a \),\( b \), and \( c \) are constants, and \( x \) is the variable. In this case, \( a = 0.60 \), \( b = 0 \), and \( c = 72 \). We simplify the equation by isolating the variable on one side. Operations such as multiplication, division, addition, and subtraction help in balancing the equation. } ], {

Algebraic solutions provide a methodical way to solve for unknowns. Once we have our linear equation set up, \[ 0.60 \times P = 72 \], the next step is to isolate \( P \).

• We divide both sides by 0.60 to isolate \( P \).
• This can be written as: \[ P = \frac{72}{0.60} \]

Division by decimals can be tricky, but using a calculator or performing the calculation step by step will yield the answer. In this case:

\[ P = \frac{72}{0.60} = 120 \]

It's important to reverse the operations in the equation to successfully isolate the variable. Focus on maintaining the balance of the equation. } ], {

Verification is crucial to ensure that our solution is correct.

To verify the result:

• We substitute \( P = 120 \) back into the original percentage equation.
• Calculate \( 60\text{\text{%}} \) of the original price, 120, to check if we get 72.
• Perform the calculation: \[ 0.60 \times 120 = 72 \]

The left side of the equation matches the right side, meaning our solution is correct. Verification gives us confidence that our algebraic manipulations and calculations are accurate. Always revisit the initial problem to confirm that your answer makes sense in the given context. } ] } } ] } ] } } ] } } ] } ] } } } ] } } } ] ] } ] } } ] } ] } } ] ]} ] } ] ] } ] } ] } ] } }] } ] } : } ] } } ] ] }] } } ] } } } } } } } } } } }] } } } } } } } } } } } } ] } } 韰� } } 賯 : } } ] }} } ]}} } } }} } } ]> }] } } } }} }}} } }}} l茅: } }} } 欤� } }}爻 }銈� ]}銉唥} 銇� } 嗒� }} 谞讻]}]-] } . ] } } } ]] {}} [] ]] json ]<|vq_11689|> [{'facet':['at','the','subject...]}鞛愲彊彀╙ functools...]+ json ] -api 鍝侅偓]}}...+ [{}}歆�]...霌滌�憓...鞁濎柎}+ [ }}}鞀惦媹雼�]...] sorted ] argmax]毽�: {}}}f...霊恾]+'{}}毽�-zero autos] {'itoproject]鞚� 鞚碷,'霝� 鞚�')=_directory+API'鞐�... } json signature }.],)))...} [靹膘灔.cleaned,'} json} 鞚� '鞗愱赴'] +...info } map},`JSON]}>] SNP]}])/ org API] ] Facet] ).). 欷戩殧毳检磮.....]} ] text 頇滌毄頃滊嫟.'}]'])} json]}] 韸轨垬觳榣e ]. } ]]}iction .+ } }}/ json %} } +} ...+ json json % ' ]電� ']}].-auto...]} json json Office '}{}} #,/ ]鞚� }] '}/.'} 雼れ潓...} )}甑愴暅.]}}} ' 毽�氍�,]} json json...]}}}+ 氤胳棎]} 娓�...}`keyword 鞚挫毄}- ' 26]} }] elder. }}歆� json 頇滌毄} }} ... json json summary]+} 雼�.'}} result } 攴� to }.] }\(. 鞚� ''}/ 氤鸽嫟, ]頃� json json np} json json]}}鞝�,<|vq_10556|>}],} json json... json json json \)(' /鞝曤炒順� json json 瓯办牅歆� json }}}'-鞏� {.})) json json }])]}