Math Problem Statement

A store sold P60 worth of chocolate bars and candies. If the chocolate bars were worth 5 times more than the candies, how much of each kind did the store sell?

Solution

Let's define the variables:

  • Let cc be the amount of money worth of candies sold (in pesos).
  • Let bb be the amount of money worth of chocolate bars sold (in pesos).

Step 1: Set up the equations

According to the problem, we have two conditions:

  1. The total sales for both chocolate bars and candies is P60: c+b=60c + b = 60

  2. The chocolate bars were worth 5 times more than the candies: b=5cb = 5c

Step 2: Solve the system of equations

We can substitute the second equation b=5cb = 5c into the first equation.

Substitute b=5cb = 5c into c+b=60c + b = 60:

c+5c=60c + 5c = 60

Now, combine like terms:

6c=606c = 60

Divide both sides by 6:

c=10c = 10

Now that we have the value for cc (candies), we can find the value for bb (chocolate bars) using b=5cb = 5c:

b=5(10)=50b = 5(10) = 50

Conclusion

  • The store sold P10 worth of candies.
  • The store sold P50 worth of chocolate bars.

Would you like any further explanation or details on this solution?


Here are 5 related questions:

  1. What if the chocolate bars were worth 3 times more than the candies? How much of each would the store sell?
  2. If the total sales were P100 instead of P60, how would the amounts change?
  3. What if the candies were worth 4 times more than the chocolate bars? What would the new amounts be?
  4. Can you determine how many units of each item were sold if you knew the price per unit?
  5. What if the problem stated that the chocolate bars were worth twice as much as the candies?

Tip: Always express one variable in terms of the other when dealing with linear equations in word problems.

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Math Problem Analysis

Mathematical Concepts

Linear equations
Proportions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9