Math Problem Statement

Lawrence buys his friends candy in the morning for $4 a box, but forgot some of his friends, so he went back to the candy shop and purchased the same candy but they had increased in price. He paid $6 a box. Let t represent the number of boxes of candy Lawrence purchased.

Write an expression that represents these purchases.

Solution

To represent Lawrence's purchases, we can break the problem into two parts:

  1. Morning purchases: Lawrence buys a certain number of boxes of candy at $4 per box.
  2. Later purchases: He buys more boxes of candy at $6 per box.

Let:

  • t1t_1 be the number of boxes Lawrence purchased in the morning (at $4 per box).
  • t2t_2 be the number of boxes Lawrence purchased later (at $6 per box).

The total cost of his purchases is:

4t1+6t24t_1 + 6t_2

If tt represents the total number of boxes of candy Lawrence purchased, then:

t=t1+t2t = t_1 + t_2

Thus, the total cost expression for Lawrence's candy purchases is:

4t1+6t24t_1 + 6t_2

Would you like more details on how to manipulate or expand this equation? Here are 5 related questions:

  1. How can we solve for t1t_1 and t2t_2 if we know the total cost Lawrence spent?
  2. What if the total number of boxes purchased, tt, is given? How can we adjust the expression?
  3. How would this change if Lawrence got a discount on the second purchase instead of a price increase?
  4. What if Lawrence buys in bulk, say 10 boxes at once, how would that impact the calculation?
  5. Can you generalize the formula for any two different prices per box?

Tip: When breaking down costs, separating the variables by time or price changes helps keep equations manageable.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Total cost = 4t1 + 6t2
t = t1 + t2

Theorems

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Suitable Grade Level

Grades 6-8