8.EE - Analyze and solve linear equations and pairs of simultaneous linear equations. Stationery Problem

7. Solve linear equations in one variable. a.Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). a. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms

Stationery Problem Lindsey and Courtney used their new boxes of stationery to write letters for Valentine's Day rather than send cards. Lindsey wrote three-page letters, and Courtney wrote one- page letters. Courtney used all the envelopes in her box and had 50 sheets of paper left over. Lindsey used all the paper in her box and had 50 envelopes left over. If the two boxes were exactly the same, how many sheets of paper were in each box?

Reasoning Abstractly and Quantitatively 1. Explain how the equation below models the following statement: ‘Courtney used all the envelopes in her box and had 50 sheets of paper left over.’ What does x+50 represent? What does x represent? What does y represent?

Reasoning Abstractly and Quantitatively 2. Explain how the equation below models the following statement: ‘Lindsey used all the paper in her box and had 50 envelopes left over.’ What does x represent? What does y/ represent? What does y/3 represent? What does y represent?

Reasoning Abstractly and Quantitatively 2.Explain how the two expressions model the same situation in the context of the problem.

Lindsey and Courtney used their new boxes of stationery to write letters for Valentine's Day rather than send cards. Lindsey wrote three-page letters, and Courtney wrote one-page letters. Courtney used all the envelopes in her box and had 50 sheets of paper left over. Lindsey used all the paper in her box and had 50 envelopes left over. If the two boxes were exactly the same, how many sheets of paper were in each box? Reasoning Abstractly and Quantitatively What values for x and y make both equations true?

Lindsey and Courtney used their new boxes of stationery to write letters for Valentine's Day rather than send cards. Lindsey wrote three-page letters, and Courtney wrote one-page letters. Courtney used all the envelopes in her box and had 50 sheets of paper left over. Lindsey used all the paper in her box and had 50 envelopes left over. If the two boxes were exactly the same, how many sheets of paper were in each box? Reasoning Abstractly and Quantitatively How many sheets for paper where in the box ?