Transcript Stationery Problem

Stationery Problem
8.EE - Analyze and solve
linear equations and
pairs of simultaneous
linear equations.
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 onepage 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.’
y = x + 50
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.’
y
+ 50 = x
3
Reasoning Abstractly and Quantitatively
2. Explain how the two expressions model the
same situation in the context of the problem.
y
# of letters written by Courtney :
3
1
# of envelopes used by Courtney : y
3
Reasoning Abstractly and Quantitatively
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?
What values for x and y make both equations true?
y = x + 50
y
+ 50 = x
3
Reasoning Abstractly and Quantitatively
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?
How many sheets for paper where in the box ?
y = x + 50
y
+ 50 = x
3