Write and evaluate the expression. Then, select the correct answer.
ten times the sum of seven and a number, evaluate when j = 1
Replace With 10 Key Words
ten times the sum of seven a number X+7J)
A. 10 x 7+j; when j = 1, the value is 71
B . 7(10+j); when j = 1, the value is 77
C. 10(7-j); when j = 1, the value is 60
D. 10(7+j); when j = 1, the value is 80
The Correct Answer and Explanation is:
The given expression is described as “ten times the sum of seven and a number.” This means that we are multiplying the sum of 7 and a number by 10. To express this algebraically, let’s define the unknown number as ( j ), and the expression would be:
[
10 \times (7 + j)
]
This represents “ten times the sum of seven and the number ( j ).”
Now, let’s evaluate the expression when ( j = 1 ).
Substitute ( j = 1 ) into the expression:
[
10 \times (7 + 1) = 10 \times 8 = 80
]
So, when ( j = 1 ), the value of the expression is 80.
Evaluation of the Given Choices:
- Option A: ( 10 \times (7 + j) ) when ( j = 1 ), the value is 71. This is incorrect because the correct value is 80, not 71.
- Option B: ( 7 \times (10 + j) ) when ( j = 1 ), the value is 77. This expression is incorrect because it changes the structure of the original problem and doesn’t reflect “ten times the sum of seven and a number.”
- Option C: ( 10 \times (7 – j) ) when ( j = 1 ), the value is 60. This is incorrect because it uses subtraction instead of addition, leading to a different value.
- Option D: ( 10 \times (7 + j) ) when ( j = 1 ), the value is 80. This is the correct expression and correctly gives the value 80 when ( j = 1 ).
Correct Answer:
The correct answer is D: ( 10 \times (7 + j) ), and when ( j = 1 ), the value is 80.
This expression follows the structure described in the problem—multiplying the sum of 7 and ( j ) by 10—and the calculation is correct when ( j = 1 ).