application problems with consecutive integers

1. EQUATIONSWITH
APPLICATION
Sections 2.1-2.4

2. Expectations to Solve
■ Define a variable
■ Write out the equation
■ Work to solve the equation
■ Answer in a sentence

3. Example:
Chris has saved twice the number of quarters
that Nora saved plus 6.The number of
quarters Chris saved is also five times the
difference of the number of quarters and 3
that Nora saved.Write and solve an equation
to find the number of quarters they each
saved.

4. Chris has saved twice the number of quarters that Nora saved plus 6.The number of quarters Chris
saved is also five times the difference of the number of quarters and 3 that Nora saved.Write and
solve an equation to find the number of quarters they each saved.
Define your variable
Let q = the number of quarters Nora saved
We are given the number of quarters Chris saved in terms of the number Nora saved.
If we knew how many Nora saved we could solve directly for the number that Chris saved.

5. Chris has saved twice the number of quarters that Nora saved plus 6.The number of quarters Chris
saved is also five times the difference of the number of quarters and 3 that Nora saved.Write and
solve an equation to find the number of quarters they each saved.
Translate into an equation
Chris has saved twice the number of quarters that Nora saved plus 6
𝐶ℎ𝑟𝑖𝑠 ℎ𝑎𝑠 𝑠𝑎𝑣𝑒𝑑 2𝑞 + 6
Chris saved is also five times the difference of the number of quarters and 3 that Nora saved
𝐶ℎ𝑟𝑖𝑠 𝑠𝑎𝑣𝑒𝑑 5(𝑞 − 3)
2𝑞 + 6 = 5(𝑞 − 3)

6. 2𝑞 + 6 = 5(𝑞 − 3)
Work to solve the equation
2𝑞 + 6 = 5𝑞 − 15
−2𝑞 −2𝑞
6 = 3𝑞 − 15
+15+15
21 = 3𝑞
÷ 3÷ 3
7 = 𝑞

7. 7 = 𝑞
Earlier we Let q = the number of quarters Nora saved
Therefore Nora saved 7 quarters.
Recall our problem said, “Write and solve an equation to
find the number of quarters they each saved.”

8. Recall our problem said, “Write and solve an equation to
find the number of quarters they each saved.”
Use Nora saved q=7 quarters and 𝐶ℎ𝑟𝑖𝑠 ℎ𝑎𝑠 𝑠𝑎𝑣𝑒𝑑 2𝑞 + 6
2𝑞 + 6
2(7) + 6
14 + 6
20
𝐶ℎ𝑟𝑖𝑠 𝑠𝑎𝑣𝑒𝑑 20

9. Answer in a full sentence
Nora saved 7 quarters and Chris saved 20 quarters.

10. Homework
Complete virtual worksheet