SOMATH Journal · Regents Algebra I · Part IV
August 2026 Algebra 1 Regents: Part IV
This August 2026 Algebra I Regents Part IV walkthrough covers a two-variable price system, a claim check, and algebraic elimination. Read the original questions and answer choices, then select the blue Answer control for a step-by-step SOMATH explanation: identify the idea, show the work, and check the result.
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Questions, data, and original figures are reproduced from the August 18, 2026 Algebra I examination in the NYSED Algebra I archive, with mathematical notation and layout normalized for the web. The explanations are original SOMATH teaching solutions, not official NYSED explanations or scoring rubrics. Results were checked against the NYSED scoring key and rating guide.
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Modeling and solving a price systemQuestion 35
Miguel is in charge of buying snacks for his office’s morning meetings. On Monday, he buys six muffins and four doughnuts for $20.70. On Tuesday, at the same store, he buys three muffins and six doughnuts for $21.51. There is no sales tax.
If \(m\) represents the cost of one muffin and \(d\) represents the cost of one doughnut, write a system of equations to represent this situation.
Miguel thinks one muffin costs $2.07 and one doughnut also costs $2.07. Is Miguel correct? Justify your answer.
Use your system of equations to algebraically determine the exact price of one muffin and the exact price of one doughnut.
Answer
Answer: \(6m+4d=20.70\), \(3m+6d=21.51\); Miguel is incorrect; muffin $1.59, doughnut $2.79.
- Use quantity times price for each purchase: Monday gives \(6m+4d=20.70\), and Tuesday gives \(3m+6d=21.51\).
- Test Miguel's claim in both equations. Monday would cost \(10(2.07)=20.70\), but Tuesday would cost \(9(2.07)=18.63\), not $21.51. Therefore he is incorrect.
- Eliminate muffins. Double Tuesday's equation: \(6m+12d=43.02\). Subtract Monday's equation to get \(8d=22.32\).
- Divide by 8: \(d=2.79\). Substitute into Monday's equation: \(6m+4(2.79)=20.70\), so \(6m=9.54\) and \(m=1.59\).
- Check both totals: \(6(1.59)+4(2.79)=9.54+11.16=20.70\), and \(3(1.59)+6(2.79)=4.77+16.74=21.51\).
- Answer in context: one muffin costs $1.59, and one doughnut costs $2.79. The prices are exact to the cent, not rounded estimates.
SOMATH takeaway: A proposed solution must satisfy every equation. Passing one purchase is not enough.
Answer key
Keep the key closed until you have tried the questions. Open the individual answers above for the full reasoning.
Show answer key
Q35: \(6m+4d=20.70\), \(3m+6d=21.51\); Miguel is incorrect; muffin $1.59, doughnut $2.79.
Class review: what to remember
Translate each purchase into quantity times unit price. Test a proposed solution against both purchases, not only one. Elimination combines entire equations; subtraction must affect every term. Finally, substitute the two prices into both original equations to check the arithmetic and the modeling.
Quick questions and answers
What is the answer to Question 35?
A muffin costs $1.59 and a doughnut costs $2.79. Miguel's claim that both cost $2.07 is incorrect. (NYSED scoring materials)
What system models the snack purchases?
The equations are 6m+4d=20.70 and 3m+6d=21.51, where m and d are the unit prices in dollars.
Why does Miguel's claim fail?
The proposed price $2.07 matches Monday's ten-item purchase but makes Tuesday's nine-item purchase cost $18.63, not $21.51.
How does elimination solve the system?
Double Tuesday's equation, then subtract Monday's equation. This gives 8d=22.32, so d=2.79. Substitution then gives m=1.59.
What should a complete response include?
Write both equations, justify why Miguel is incorrect, show algebraic steps for both prices, and identify which price belongs to which snack. The question is worth 6 credits.