DSC1520 Assignment 1 Semester 1 2022 Solutions (TO BE USED AS A GUIDELINE ONLY)

Quantitative Modelling 1
DSC1520
Department of Decision Sciences
Assignment 01 for Semester 01 (compulsory)
Unique Number: N/A
Due Date:
Terms of use:
• To be used ONLY for comparison purposes (As a guideline)
• Do not duplicate or distribute without written consent from the author. (That includes
distribution on WhatsApp/Telegram etc.



Question 1
𝑡+𝑎
Rewriting the equation 𝑉 = , with 𝑡 in terms of 𝑉 , gives
𝑡−𝑎
𝑉+1
1. 𝑡 =
𝑉−1
𝑎
2. 𝑡 =
𝑉−1
𝑎(𝑉+1)
3. 𝑡 =
𝑉−1
𝑎(𝑉−1)
4. 𝑡 =
𝑉+1
Answer:

𝑡+𝑎
𝑉=
𝑡−𝑎
𝑡+𝑎
Rewrite the equation as =𝑉
𝑡−𝑎
Find the LCD of the terms in the equation. Finding the LCD of a list of values is the same as
finding the LCM of the denominators of those values.

𝑡 − 𝑎, 1

,Remove parentheses.
𝑡 − 𝑎, 1
The LCM of one and any expression is the expression.
𝑡−𝑎
𝑡+𝑎
Multiply each term in = 𝑉 by 𝑡 − 𝑎 to eliminate the fractions.
𝑡−𝑎
𝑡+𝑎
(𝑡 − 𝑎) = 𝑉(𝑡 − 𝑎)
𝑡−𝑎
Simplify the left side.

Cancel the common factor of 𝑡 − 𝑎.



Rewrite the expression.

𝑡 + 𝑎 = 𝑉 (𝑡 − 𝑎)
Simplify the right side.
Apply the distributive property.

𝑡 + 𝑎 = 𝑉𝑡 + 𝑉(−𝑎)
Rewrite using the commutative property of multiplication.

𝑡 + 𝑎 = 𝑉𝑡 − 𝑉𝑎
Solve the equation.

Subtract 𝑉𝑡 from both sides of the equation.

𝑡 + 𝑎 − 𝑉𝑡 = −𝑉𝑎
Subtract 𝑎 from both sides of the equation.

𝑡 − 𝑉𝑡 = −𝑉𝑎 − 𝑎
Factor 𝑡 out of 𝑡 − 𝑉𝑡.
Factor 𝑡 out of 𝑡 1 .

𝑡 × 1 − 𝑉𝑡 = −𝑉𝑎 − 𝑎

, Factor 𝑡 out of −𝑉𝑡 .

𝑡 × 1 + 𝑡(−𝑉) = −𝑉𝑎 − 𝑎
Factor 𝑡 out of 𝑡 × 1 + 𝑡(−𝑉).
𝑡(1 − 𝑉) = −𝑉𝑎 − 𝑎
Divide each term in 𝑡(1 − 𝑉) = −𝑉𝑎 − 𝑎 by 1 − 𝑉 and simplify.
𝑡(1 − 𝑉) −𝑉𝑎 −𝑎
= +
1−𝑉 1−𝑉 1−𝑉
Simplify the left side.

Cancel the common factor of 1 − 𝑉.




Divide 𝑡 by 1.

−𝑉𝑎 −𝑎
𝑡= +
1−𝑉 1−𝑉
Simplify the right side.
Combine the numerators over the common denominator.

−𝑉𝑎 − 𝑎
𝑡=
1−𝑉
Factor 𝑎 out of −𝑉𝑎 − 𝑎.
Factor 𝑎 out of −𝑉𝑎.

𝑎(−𝑉) − 𝑎
𝑡=
1−𝑉
Factor 𝑎 out of −𝑎.

𝑎(−𝑉 ) + 𝑎 × −1
𝑡=
1−𝑉