algebra questions

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HW #5 – MATH-105-01
The demand and supply functions of a product are given. In each case, p represents the price in
dollars per unit and x represents the number of units in hundreds. Find the equilibrium point.
(Worth 4 points)
1) 7p+ x = 150 Demand equation
10p – x = 20 Supply equation
Solve each system by any method. (Each worth 4 points)
2) –3x + 3y=-3
12x – 10y = 34
3) –2x+2y= 6
-2x+6y= 30
4) Castel’s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 8
senior citizen tickets and 10 student tickets for a total of $160. The school took in $125 on the
second day by selling 1 senior citizen ticket and 10 student tickets. What is the price each of one
senior citizen ticket and one student ticket?
5) The senior classes at High School A and High School B planned separate trips to the county fair. The
senior class at High School A rented and filled 11 vans and 14 buses with 742 students. High School
B rented and filled 11 vans and 6 buses with 406 students. Each van and each bus carried the same
number of students. Find the number of students in each van and in each bus.
6) Jared’s Youth League basketball team scored on 27 shots, some two-point field goals and the rest
one-point free throws. The team scored a total of 48 points in the game. How many of each kind of
shot was made?
7) Two angles are supplementary. (Supplementary angles are angles whose sum is 180°.) Their
difference is 22°. Find the angles.
8) Rick’s Sporting Goods ran a promotion offering either a free rechargeable lantern or a free portable
propane grill to each customer who bought a deluxe family tent. The store’s cost for each lantern was
$20, and its cost for each grill was $25. At the end of the promotion, 12 tents had been sold. The
store’s total cost for the items given away was $280. How many of each type of free item did the
customers choose?
9) An executive nearing retirement made two investments totaling $45,000. In one year, these
inestments yielded $2430 in simple interest. Part of the money was invested at 4% and the rest at
6%. How much was invested at each rate?
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Ꮅ•••••
10) 4r + s + 6t = 21
S=-5
t=-2r – 38 – 4
11) -6a + 8b+ 6c = 28
ба – 5b – Зc = -25
-6a + 2b – 4c = 26
12) 2b + 50 =-4
-2a – b + 4c = 10
a + 4b – 5c = -12
13) 6r+s- 2t=-9
-5r-s=1
-5r + s + 2t = 7
1
13
14) -a +-b-cr-
2 2
2
1
-a –
C=-5
3
3 3 2
a – – +
C=-
5 5 5 5
b
4
15) 2r + t = 2
3
1
29
-r+ s + 3t = –
2
2
4
4
–rs–t= -5
3
16) x = 6y + 2
y=-62 + 5
0.8x – z=-4.2
17) 2a + 0.8c = -6
a = 2b-c-11
b=-2a – 2
18) The sum of three number is 55. The difference of the largest and the smallest is 49, and the sum of
the two smaller is 13. Find the numbers.
19) In a game,
the
top three rushers for the Redskins in their victory against the Vikings totaled 129
yards. Chris Thompson had 18 more yards than Jamison Crowder. Crowder had 90 yards less than
Robert Kelley. How many yards did each player get in the game?
Use the compound interest formula (2 points each)
20) INVESTMENT. How much should a
mother invest at the time her son is born to
provide him with $80,000 at age 21?
Assume that the interest is 7% compounded
quarterly.
21) INVESTMENT. Ms. Ann Scheiber retired
from goverment service in 1941 with a
montly pension of $83 and $5000 in
savings. At the time of her death in January
1995 at the age of 101, Ms. Scheiber had
turned the $5000 in $22 million through
shrewd investments in the stock market.
She bequeathed all of it to Yeshiva
University in New York City. What annual
rate of return compounded annually would
turn $5000 to a whopping $22 million in 54
years?