1078 Basic Algebra questions: solving an equation, equalities and inequalities
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Edward Morey October 6, 2006
(note that the questions are numbered in groups)
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Solve for the indicated variable in terms of the remaining variables:
- A= P+Prt; for r
; for m
- Solve for x:
- Solve this equation for u:
times on both sides à
- You need a compressor and there are two choices for you. You can rent a compressor for the cost of $90/day. Alternatively, you can buy one at $4,000 with maintenance costs around $10/day. Let X denote the number of days that the compressor is needed. Find out the value of X that makes these two choices equivalent.
Total cost for buying a compressor after x days: 4,000+10x
Total cost for renting one after x days: 90x
Set two costs function equalized and solve for x:
4000+10x = 90x à 80x=4000 à x=50 days
- Solve for x.
(A)
(B)
(C)
- Supply and demand
Suppose that the supply and demand equations for printed T-shirts in a little town during Christmas week are
Supply: p = q + 12
Demand: p = - 2q + 36
Where p is the price in dollars and q is the quantity in hundreds.
A) Find the supply and demand quantity if p = $16.
B) Find the equilibrium price and quantity. (when the price of supply equals the price of demand).
1. Solve.
A
Solve and graph
1.
A
( ]
–2 8 x
- Solve the inequality for y and graph your answer:
A
( ]
–9 6 y
- You need a compressor and there are two choices for you. You can rent a compressor for the cost of $80/day. Alternatively, you can buy one at $7,000 with maintenance costs around $10/day. Let X denote the number of days that the compressor is needed. Find out the value of X that makes these two choices equivalent.
A Solving , x = 100 days.
Check the following equalities.
1.
2.
3. 3(x-2 ) = 2(x-3) + x
4.
5.
6.
Demonstrate the equalities:
- Solve the inequality for y and graph your answer:
or
Solve for x:
1.
2.
3.
4.
1. The supply for broccoli is described by the equation Q = P/6 where P is the price of broccoli and Q is the amount that will be supplied at price P. The demand equation is described by Q = 330-9P where P is the price of broccoli and Q is the amount that will be demanded. What is the equilibrium PRICE of broccoli where demand equals supply?
2. Solve for y in terms of x the expression
3. Solve by factoring:
A (Since ,)
4. Solve using the quadratic formula
A
5. Suppose the demand equation (inverse demand function) is written as:
And the supply equation is:
What is the equilibrium price p when D = S. (Choose only the positive price.)
A (By ,) .
- Solve this equation for u:
A times on both sides à
- Solve for x:
A