# How do you solve mixture problems using a system of equations?

Last updated date: 17th Mar 2023

•

Total views: 204k

•

Views today: 1.83k

Answer

Verified

204k+ views

**Hint**: Mixture problems are ones where two different solutions are mixed together resulting in a new final solution. We generally use a table to solve mixture equations and plot the different variables as per the criteria given to arrive at a rational conclusion.

**:**

__Complete step-by-step answer__A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Mixture equation is generally solved by using the following table format:

Amount | Part | Total | |

Item 1 | |||

Item 2 | |||

Final |

The first column is for the amount of each item we have. The second column is labelled “part” which can be generally in form or percentage or any other criteria. To arrive at the total, we simplify having to multiply the “Amount” and “Part”. We can get an equation by adding the amount and/or total columns that will help us solve the problems. These problems can have either one or two variables.

Let us understand with the help of an example:

A chemist has \[70\]mL of a \[50\% \] methane solution. How much of the \[80\% \] solution must she add so the final solution is \[60\% \] methane?

Step 1: Construct the mixture table with the given data. We start with \[70\], but don′ t know how much we add, that is \[x\]. The part is the percentages, \[0.5\] for start, \[0.8\] for add.

Qty(ml) | % | Total | |

Start | \[70\] | \[0.5\] | |

Add | \[x\] | \[0.8\] | |

Final |

Step 2: Add the values to arrive at the final column. The percentage for this quantity is \[0.6\] because we want the final solution to be \[60\% \] methane.

Qty(ml) | % | Total | |

Start | \[70\] | \[0.5\] | |

Add | x | \[0.8\] | |

Final | \[70 + x\] | \[0.6\] |

Step 3: Multiply the quantity with % to arrive at the total column.

Qty(ml) | % | Total | |

Start | \[70\] | \[0.5\] | \[35\] |

Add | \[x\] | \[0.8\] | \[0.8x\] |

Final | \[70 + x\] | \[0.6\] | \[42 + 0.6x\] |

Step 4: Now we can construct an equation:

\[35 + 0.8x = 42 + 0.6x\]

Subtracting by \[0.6\]on both the sides,

\[35 + 0.2x = 42\]

Further simplifying

\[0.2x = 42 - 35\]

\[0.2x = 7\]

\[x = \dfrac{7}{{0.2}}\]

\[x = 35\]

Hence, we can conclude that a \[35\] ml solution will be required.

**So, the correct answer is “\[35\] ml”.**

**Note**: Mixture problems can be solved easily by drawing a table and then applying simple addition, subtraction, multiplication and division rules. There may be more than one unknown variable which can be found as per the above method. Mixture problems are used practically in a variety of fields for solving real life problems for example concentration of acid in a solution, finding value of product in staggered price structure, deciding discount policy for product based on given margin etc.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?