MAT 114– Prof. Bui Name ______
Section 3.4 Applications of Linear Systems
Steps:
- Read and underline important terms
- Assign 2 variables x and y (use diagram or table or drawing as needed)
- Write a system of equations
- Solve for the variables
- Check your answers
- State your answers
PROBLEMS WITH QUANTITIES AND COST
1) In a city, the adult movie ticket costs $10 and child ticket costs $8. If an extended family and friends of 36 people paid $298 for tickets to see The Titanic, how many adults and how many children were there?
2) A restaurant offers two special meals “California Sushi rolls” meal for $12.99 each and “Shrimp Sushi rolls” meal for $19.99 each (disregarding tax). In one day, the restaurant sold 40 total meals and collected a total of $694.60. How many of each type of meal did they sell?
PROBLEMS WITH MIXTURES
3) How many liters of 25% alcohol solution must be mixed with 12% solution to get 13 liters of 15% solution?
4) A pharmacist needs 100 gallons of 50% alcohol solution. She has available a 30% solution and an 80% solution. How much of each should she use?
5) I want to mix the $4 per pound coffee with 20 pounds of coffee worth $7 per pound to get a mixture that can be sold for $5 per pound. How many of the cheaper coffee should I use?
PROBLEMS WITH SIMPLE INTEREST
6) A student borrows a total of $9600 for both Perkin loan and Stafford loan. If the Perkin loan (P.L.) has a 5% simple interest and Stafford loan (S.L) has a 8% simple interest, what was the original amount of each loan if the total interest after one year is $633.
7) $5000 is invested, part of it at 3% and part of it at 1.5%. For a certain year, the total simple interest is $90. How much was invested at each rate?
MOTION PROBLEMS
8) In one hour Ann can row 2 miles against the current or 10 miles with the current. Find the speed of the current and the speed of Ann’s boat in still water?
Let
Distance =(d) / Rate *
(r) / Time
(t)
With Current
Against Current
Equations:
9) Two airplanes leave Boston at 12:00 noon and fly in opposite directions. If one flies at 410 mph and the other 120 mph faster, how long will it take them to be 3290 miles apart?
Let
Distance =(d) / Rate *
(r) / Time
(t)
With Current
Against Current
Equations:
10) A bus leaves downtown terminal, traveling east at 35 mph. One hour later, a faster bus leaves downtown, also traveling east on a parallel tract at 40 mph. How far from the downtown will the faster bus catch up with the slower one?
Let
Distance =(d) / Rate *
(r) / Time
(t)
With Current
Against Current
Equations: