Can an algebraic expression be made here.

  • Context: MHB 
  • Thread starter Thread starter mathlearn
  • Start date Start date
  • Tags Tags
    Expression
Click For Summary
SUMMARY

The discussion centers on formulating a Diophantine equation to determine the number of mandarins and guavas that can be purchased for a total of 50 currency units. The prices are set at 20 for a mandarin and 15 for a guava, leading to the equation 20M + 15G = 50. Simplifying this equation by dividing through by 5 results in 4M + 3G = 10. This simplification confirms that the equation is in its maximum simplified form.

PREREQUISITES
  • Understanding of Diophantine equations
  • Basic algebraic manipulation skills
  • Familiarity with variables in mathematical expressions
  • Knowledge of linear equations
NEXT STEPS
  • Study the properties of Diophantine equations
  • Learn methods for solving linear equations with two variables
  • Explore integer solutions in algebraic contexts
  • Investigate applications of algebra in real-world scenarios
USEFUL FOR

Students, mathematicians, and anyone interested in algebraic problem-solving, particularly in the context of purchasing scenarios and integer solutions.

mathlearn
Messages
331
Reaction score
0
The price of a mandarin is 20 and the price of a guava is 15. Find the number of mandarins and guavas that can be bought for 50.

(Thinking) So can an algebraic expression be made and the number of mandarin's and guavas that can be bought for 50.

Many Thanks (Happy)
 
Mathematics news on Phys.org
Well, let $M$ be the number of mandarins and $G$ be the number of guavas, then we have:

$$20M+15G=50$$

Divide through by 5:

$$4M+3G=10$$

This is a Diophantine equation.
 
MarkFL said:
Well, let $M$ be the number of mandarins and $G$ be the number of guavas, then we have:

$$20M+15G=50$$

Divide through by 5:

$$4M+3G=10$$

This is a Diophantine equation.

Many Thanks (Happy), So I see that this is the maximum the equation can be simplified.
 

Similar threads

MHB Problems leading to quadratic equation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Expressing any given point on plane with one unique number
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Do You Calculate Loss Percentage in a Quadratic Equation Problem?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solving Equation (Application)
  • · Replies 6 ·
Replies
6
Views
2K
MHB Few more questions from 6th Grade text onward ,Please help ?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Algebraic expression simplification 2(2u+v)/u = 4(v^2-4u^2)/3u^2
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What is the role of geometry and dimensional operations?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Expression, Terms, Factors, Coefficients, Mono/Bi/Poly HELP
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Much Equity Is Needed for Buying a Second Property?
  • · Replies 5 ·
Replies
5
Views
2K
MHB How Can Terrific Wears Inc. Maximize Revenue and Profit from Suit Sales?
  • · Replies 3 ·
Replies
3
Views
4K