Answer:
A:
Dylan’s weight is d.
Twice Dylan’s weight is 2d.
Three pounds more than twice Dylan’s weight is 2d + 3.
So, the expression for Alan’s weight in terms of Dylan’s weight is 2d + 3.
B:
Dylan’s weight is d.
Three times Dylan’s weight is 3d.
Twelve less than three times Dylan’s weight is 3d − 12.
So, the expression for Bruce’s weight in terms of Dylan’s weight is 3d − 12.
C:
Cecil’s weight is the sum of Alan's weight and Bruce's weight.
Alan’s weight in terms of Dylan's weight is 2d + 3.
Bruce’s weight in terms of Dylan's weight is 3d − 12.
So, the expression for Cecil’s weight in terms of Dylan’s weight is (2d + 3) + (3d − 12).
D:
Cecil's weight is (2d + 3) + (3d − 12).
Find Cecil's weight by substituting Dylan’s weight (d = 45) into the expression above:
(2 × 45 + 3) + (3 × 45 − 12)
= (90 + 3) + (135 − 12)
= 93 + 123
= 216.
If Dylan weighs 45 pounds, then Cecil weighs 216 pounds.
E:
Yes, the expression can be simplified by using the Associative and Commutative Properties of addition and by combining the like terms in the expression.
F:
(2d + 3) + (3d − 12)
First remove the parentheses:
2d + 3 + 3d − 12.
Then group the like terms:
2d + 3d + 3 − 12.
Finally, add and subtract the like terms:
5d − 9.
The expression (2d + 3) + (3d − 12) simplifies to 5d − 9.
G:
Cecil’s weight in terms of Dylan’s weight is 5d – 9.
Find Cecil’s weight by substituting Dylan’s weight (d = 45) into the expression above:
(5 × 45) − 9
= 225 − 9
= 216.
If Dylan weighs 45 pounds, then Cecil weighs 216 pounds.
H:
Yes, the answers are the same. The expression from part D is equivalent to the expression from part G.
I:
Bruce's weight in terms of Dylan’s weight is 3d − 12.
Alan's weight in terms of Dylan’s weight is 2d + 3.
So, the expression (3d − 12) − (2d + 3) represents how much more Bruce weighs than Alan.
J:
The expression is (3d − 12) − (2d + 3).
Evaluate the expression by substituting Dylan’s weight (d = 45) into it:
(3 × 45 − 12) − (2 × 45 + 3)
= (135 − 12) − (90 + 3)
= (123) − (93)
= 30.
Bruce weighs 30 pounds more than Alan weighs.
K:
The expression (3d − 12) − (2d + 3) simplifies to d − 15.
L:
The expression is d − 15.
Evaluate the expression by substituting Dylan’s weight (d = 45) into it:
45 − 15 = 30.
Bruce weighs 30 pounds more than Alan. This is the same answer as in part J.
Do not copy, it's the exact answer from edmuentum
