Hướng dẫn giải Bài 55 (Trang 34 SGK Toán Đại số 8, Tập 2)

Đề bài: Biết rằng 20g một dung dịch chứa 50g muối. Hỏi phải pha thêm bao nhiêu gam nước vào dung dịch đó để được một dung dịch chứa <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal">&#x0025;</mi></math>">20% muối?  Lời giải chi tiết: Gọi <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo></math>">x(g) là khối lượng nước phải pha thêm, với <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>">x>0. Khối lượng dung dịch mới là <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo>+</mo><mi>x</mi><mspace width="thickmathspace" /><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo></math>">200+x(g). Vì dung dịch mới có nồng độ <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal">&#x0025;</mi></math>">20% nên ta có phương trình: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>50</mn><mrow><mn>200</mn><mo>+</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mpadded><mfrac><mn>20</mn><mn>100</mn></mfrac></mpadded><mspace linebreak="newline"></mspace><mo>⇔</mo><mfrac><mn>50</mn><mrow><mn>200</mn><mo>+</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mpadded><mfrac><mn>1</mn><mn>5</mn></mfrac></mpadded><mspace linebreak="newline"></mspace><mo>⇔</mo><mrow><mfrac><mn>5.50</mn><mrow><mn>5</mn><mo>⁢</mo><mrow><mo>(</mo><mn>200</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mpadded><mfrac><mrow><mn>200</mn><mo>+</mo><mi>x</mi></mrow><mrow><mn>5</mn><mo>⁢</mo><mrow><mo>(</mo><mn>200</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mpadded></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>⇒</mo><mn>250</mn><mo>=</mo><mn>200</mn><mo>+</mo><mpadded><mi>x</mi></mpadded></mrow><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>250</mn><mo>-</mo><mpadded><mn>200</mn></mpadded><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>50</mn></math> (thỏa mãn) Vậy phải pha thêm <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mi>g</mi></math>">50g nước thì được dung dịch chứa <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal">&#x0025;</mi></math>">20% muối.