Math Problem Statement
Mrs. Whitson wants to buy a banner for Franklin central junior high's hallway that costs $125. She wants to give away candy bars and suckers to the most spirited students. Each candy bar costs $2 each and each sucker costs $1 each. Mrs. Whitson budget is $1,079. If she buys equal numbers of candy bars and suckers, how many of each can she afford to buy?
Solution
Let's break down the problem step-by-step to find the number of candy bars and suckers Mrs. Whitson can afford to buy.
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Total Budget: Mrs. Whitson has a total budget of $1,079.
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Cost of the Banner: The banner costs $125.
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Remaining Budget: After buying the banner, the remaining budget is:
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Cost of Candy Bars and Suckers:
- Each candy bar costs $2.
- Each sucker costs $1.
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Let be the number of candy bars and suckers Mrs. Whitson buys. Since she buys equal numbers of candy bars and suckers:
- Total cost for candy bars: dollars.
- Total cost for suckers: dollars.
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Total Cost for Candy Bars and Suckers: The combined cost for candy bars and suckers is:
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Set Up the Equation: We want to find such that the total cost does not exceed the remaining budget of $954:
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Solve for :
So, Mrs. Whitson can afford to buy 318 candy bars and 318 suckers.
Would you like a more detailed explanation or have any other questions?
Related Questions:
- What if the cost of the banner was higher or lower? How would that affect the number of candy bars and suckers she can buy?
- How would the solution change if candy bars and suckers had different costs (e.g., candy bars costing $3 each)?
- If Mrs. Whitson had a different total budget, how would you calculate the number of candy bars and suckers?
- What if Mrs. Whitson wanted to buy a different ratio of candy bars to suckers (e.g., twice as many suckers as candy bars)?
- How can we express the total number of items bought in terms of ?
Tip:
When dealing with word problems, break down the information given into smaller parts and use algebraic expressions to find a solution systematically.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Budgeting
Formulas
Remaining Budget = Total Budget - Cost of Banner
Total Cost = 2x + x = 3x
x = Remaining Budget / 3
Theorems
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Suitable Grade Level
Grades 6-8
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