Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Guided Practice 8
Page 63 Exercise 1 Answer
3(3x + 2x + x)
Write Equivalent expressions using properties
→ By Combining like terms, I can write this expression:
3(3x + 2x + x) = 3((3 + 2 + 1)x) = 3(6x)
→ By using the Distributive Properties, I can write this expression:
3(3x + 2x + x) = 3(3x) + 3(2x) + 3(x) = 9x + 6x + 3x
Result
3(6x) ; 9x + 6x + 3x
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 63 Exercise 2 Answer
I can substitute the value of x in the expression to find the number of hours Patrick plans to spend training during the summer.
3(3x + 2x + x)
= 3(3x) + 3(2x) + 3(x) Using Distributive Property
= 9x + 6x + 3x Multiply
= 18x Combining Like terms
= 18(9) Substitute x = 9
= 162
Result
Total hours Patrick plans to spend training over 9 weeks is 162 hours
Page 63 Exercise 3 Answer
(25t + 15) + (20t + 10) + 50t
Write Equivalent expressions using properties
→ By using Commutative Property, I can write this expression:
(25t + 15) + (20t + 10) + 50t = (20t + 10) + (25t + 15) + 50t
→ By Combining Like Terms, I can write this expression:
(25t + 15) + (20t + 10) + 50t = 25t + 20t + 50t + 15 + 10 = 95t + 25
Result
(20t + 10) + (25t + 15) + 50t ; 95t + 25
Page 63 Exercise 4 Answer
95t + 25 Evaluate
= 95(5) + 25 Substitute t = 5
= 475 + 25 Multiply
= 500 Add
Result
The Total cost Yolanda will pay is $500
Page 64 Exercise 5 Answer
Alex
Overtime Bonus = $10
Hourly wage = $7
Number of days = 2
Number of hours = x
Alex′s earning = Number of days(Overtime Bonus + Hourly wage ⋅ Number of hours) = 2(10 + 7 ⋅ x)
= 2(10 + 7x)
Tyrone
Overtime Bonus = $15
Hourly wage = $8
Number of days = 2
Number of hours = x
Tyrone′s earning = Number of days(Overtime Bonus + Hourly wage ⋅ Number of hours) = 2(15 + 8 ⋅ x)
= 2(15 + 8x)
Result
Alex′s earning: 2(10 + 7x)
Tyrone′s earning: 2(15 + 8x)
Page 64 Exercise 6 Answer
Mrs. Hayes accurately sum each of their wages to get the total amount she paid.
She also multiply their hourly wages with the number of hours, x
Hence, Mrs. Hayes′s expression is accurate
Result
Yes, Mrs. Hayes′s expression is accurate.
Page 64 Exercise 7 Answer
2(10 + 7x) + 2(15 + 8x)
Write Equivalent expressions using properties
→ By using the Distributive Properties, I can write this expression:
2(10 + 7x) + 2(15 + 8x) = 2(10) + 2(7x) + 2(15) + 2(8x) = 20 + 14x + 30 + 16x = 30x + 50
Result
30x + 50
Page 64 Exercise 8 Answer
If each worked 9 hours each day then we can substitute the value of x to find the total amount Mrs. Hayes paid to Alex and Tyrone.
30x+ 50
= 30(9) + 50
= 270 + 50
= $320
Result
Mrs. Hayes paid the total amount $320