Question textSuppose a little girl likes peanut butter and jelly sandwiches with exactly 2T of jelly and 1T of peanut butter. Suppose further that her mom agrees to make sandwiches to those exact specifications and the price of peanut butter is $.25/T and the price of jelly is $.10/T. If she has $1.80 to spend on peanut butter and jelly ingredients (ignore the bread) in a week, how many sandwiches will she make? Answer 1 Question 7[input]

Question

BlackTom AI · Accepted Answer

Each sandwich requires 1 T peanut butter and 2 T jelly. Unit-price multiplication and division determine how many full sandwiches the budget allows.

1) Relevant concepts: unit cost (price per tablespoon), cost per bundle (sandwich), and budget division (total budget ÷ cost per sandwich).  
2) Compute cost per sandwich step by step:
- Peanut butter: 1 T × $0.25/T = $0.25 per sandwich.
- Jelly: 2 T × $0.10/T = 2 × $0.10 = $0.20 per sandwich.
- Total cost per sandwich = $0.25 + $0.20 = $0.45.
3) Use the weekly budget to find quantity:
- Budget = $1.80. Number of sandwiches = $1.80 ÷ $0.45.
- To avoid decimals, convert to cents: 180 cents ÷ 45 cents = 4.
4) Why this answer is correct: each sandwich consumes a fixed bundle of ingredients costing $0.45. With $1.80 you can buy exactly four such bundles because 4 × $0.45 = $1.80, so you exhaust the budget making 4 full sandwiches. There is no fractional leftover because the division is exact.
5) Why other counts would be wrong:  
- 3 sandwiches would cost 3 × $0.45 = $1.35, leaving unused budget but not maximizing sandwiches.  
- 5 sandwiches would cost 5 × $0.45 = $2.25, which exceeds the $1.80 budget and therefore is infeasible.
6) Conclusion: The calculation confirms the correct number of sandwiches is 4, matching the provided answer.

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