Compute Invested Money at Each Interest Rate

Money Invested at 7% and 5% Rate Word Problem

Mr. Z invested $35,000; part at 7% and part at 5%. The total interest on both investments was $2,000. How much did he invested at each rate?

Let X = money invested at 7%

Let Y = money invested at 5%

X + Y =



Equation 1 or Given condition 1 or constraint 1 to satisfy . How much money was invested at 7% ? You don't know, you assigned this unknown as variable letter X amount of money. How much money was invested at 5 %. You don't know, you assigned this unknown as variable letter Y amount of money. But you know the total of X and Y is 35,000

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X + Y =



Equation 2 or Given condition 2 or constraint 2 to satisfy. How much interest was earned by X money invested at 7% ? You don't know yet. But you are sure it must be 7% or 0.07 times X amount. How much interest was earned by Y money invested at 5% ? You don't know yet. But you are sure it must be 5% or 0.05 times Y amount. You also know if you add all the interest earned it must be 2000. Written mathematically 0.07 X + 0.05 Y = 2000

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Answer, X invested at 7%

=

Answer, Y invested at 5%

=

To check your answer substitute the value of X and Y in both equation 1 and equation 2.
To do "what if " scenario analysis , just change any variables.

How this automatic calculation happen? Learning how to compute determinant of 2x2 matrix and applying Cramer's rule makes this automatic calculation possible. That is advance mathematics but you can visit this link to learn more. Visit Determinant of 2 x 2 Matrix for more explanation on how this automatic scenario analysis becomes possible

A solved problem becomes trusted automation—saving time and accelerating decision-making.

HOW TO USE:
Type new number in input box. Answer is automatic

IMPORTANT to enter 1 if there is no constant on X and Y. Since 1 * X = X and 1 * Y = Y
. Do not include the comma symbol , because it will display Not a Number (NaN) error message.

To check your solution, just substitute the value of X and Y in equation 1 and equation 2 both equation must be true otherwise your answer is not correct and valid.

Now student and teacher will no longer need to check the test exam paper because it is done automatically. This will save teacher a lot of time in checking paper.

Learning Algebra is very important skill every student must master. Why? Because algebra give student the training and stamina to press on , to formulate, to grapple with complex problem. It trains student to reflect on their thinking during problem solving process, develop the habits of persistent. It trains them to gather proof and evidence for critical analysis. In algebra student are given the training to analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem.

Today with machine learning and artificial intelligence the hard part of doing actual computation is now easy as you experience from using this software tool. But the concept of Algebra remains the same. Algebra connect the quantitative relationship of physical things like the invested money at 7% and 5% that you want to solve. Algebra deals with representing the physical objects as letter variable like let letter X represent the invested money at 7% and let the letter Y represent the invested money at 5%. Now the teacher job is to help the student to realize that every letter or variable they see in algebraic equation represent a physical object. Trying to convince their student that Algebra is a cool tool because when they are solving algebraic equation they are like playing with physical material in the laboratory but not spending any money for material cost because it is done using paper and pencil or simulation in computer software. Algebra is behind the computer simulation modelling.

When they actually work with actual material things their skills in using Algebra will save them time and money.

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Understanding the difference between collaboration and automation

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