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:
- Morning purchases: Lawrence buys a certain number of boxes of candy at $4 per box.
- Later purchases: He buys more boxes of candy at $6 per box.
Let:
- be the number of boxes Lawrence purchased in the morning (at $4 per box).
- be the number of boxes Lawrence purchased later (at $6 per box).
The total cost of his purchases is:
If represents the total number of boxes of candy Lawrence purchased, then:
Thus, the total cost expression for Lawrence's candy purchases is:
Would you like more details on how to manipulate or expand this equation? Here are 5 related questions:
- How can we solve for and if we know the total cost Lawrence spent?
- What if the total number of boxes purchased, , is given? How can we adjust the expression?
- How would this change if Lawrence got a discount on the second purchase instead of a price increase?
- What if Lawrence buys in bulk, say 10 boxes at once, how would that impact the calculation?
- 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
-
Suitable Grade Level
Grades 6-8
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