Download Day 4 Answer Key

Algebra Day 4
Presentation Problems
1. The sum of three consecutive integers is 405. What are the three numbers?
First integer
134
= ? (134)
Second integer
134
1
Third integer
134
405
- 3
402
= ? (135)
2
= 405
= ? (136)
3 units = 402
402 ÷ 3 = 134
Algebra
Let x = 1st integer
Let x + 1 = 2nd integer
Let x + 2 = 3rd integer
x + (x + 1) + (x + 2) = 405
3x + 3 = 405
3x = 402
x = 134
The numbers are 134, 135, and 136.
2. The sum of five consecutive integers is 465. What are the integers?
First integer
91
= ? (91)
Second integer
91
1 = ? (92)
Third integer
91
Fourth integer
91
Fifth integer
91
465
- 10
455
2
= 465
= ? (93)
3
= ? (94)
4
= ? (95)
Algebra
Let x = 1st integer
Let x + 1 = 2nd integer
Let x + 2 = 3rd integer
Let x + 3 = 4th integer
Let x + 4 = 5th integer
5x + 10 = 465
5x = 455
x = 91
5 units = 455
455 ÷ 5 = 91
The numbers are 91, 92, 93, 94, and 95.
3. Lisa is bored, riding in the backseat of her parent’s SUV on their family vacation.
She notices the mile markers on the interstate. She adds up three consecutive mile
markers and discovers the sum is 312. Which three mile marker signs did her family
just pass?
First marker
103
= ? (103)
Second marker
103
1
Third marker
103
312
- 3
309
= ? (104)
2
= 312
= ? (105)
3 units = 309
309 ÷ 3 = 103
They passed mile markers 103, 104, and 105.
Algebra
Let x = 1st integer
Let x + 1 = 2nd integer
Let x + 2 = 3rd integer
x + (x + 1) + (x + 2) = 312
3x + 3 = 312
3x = 309
x = 103
Algebra Day 4
Assessment Problems
1. The sum of three consecutive integers is 1560. What are the three numbers?
First number
519
= ? (519)
Second number
519
1
Third number
519
1560
- 3
1557
= ? (520)
2
= 1560
= ? (521)
3 units = 1557
Algebra
Let x = 1st integer
Let x + 1 = 2nd integer
Let x + 2 = 3rd integer
x + (x + 1) + (x + 2) = 1560
3x + 3 = 1560
3x = 1557
x = 519
1557 ÷ 3 = 519
The numbers are 519, 520, and 521.
2. A book is lying open so that the sum of its visible page numbers is 379. What
pages are showing?
First page
189
= ? (189)
= 379
Second page
379
- 1
378
189
1
= ? (190)
2 units = 378
378 ÷ 2 = 189
The book is open to pages 189 and 190.
Algebra
Let x = 1st integer
Let x + 1 = 2nd integer
x + (x + 1) = 379
2x + 1 = 379
2x = 378
x = 189