REVIEW 3B
Name
per.
Define the variables. Write the system of equations. Solve the system using matrices.
/
l, / An apartment building has 50 units. All are one- or two-bedroom units. One bedroom units rent
J for 5425/mo, and two bedroom units rent for 5550/mo. When all units are occupied, the total
many apartments of each type are there?
0 The perimeter of a rectangular parking lot is 216 feet. The width of the rectangle is 14 feet less than the
length. Find the area of the parki
w = L-Iÿ -i
William rowed 6 miles downstream in ¾ hour. His was exhausted during his return trip and it took him
twice as long going upstream. What was William's speed in still water and what was the speed of the
i.Se-ÿ.5c: =(0 Ll.6 -I.6
q , Paige has 68 coins in nid{els, dimes, and quarters. She has twice as many quarters as dimes and the
total value of the coins is 510.15. How many of each coin does Paige have?
: nigFds = ÿa
d :dimes: Iÿ
q uar s -
.05n ÿ. Iod +, f.6ÿ
5 .10 .ÿ5 !o,I
,/ Silo sold 3 soccer balls, a bucket of baseballs, and a case ofgolf balls for 577.50. They also sold 3 soccer balls and 2
casesÿ golf balls for 567.50. In addition, they sold a bucket of baseballs and 3 cases of golf balls for 570.00. Find the
[' cost of a socceÿost of a bucket of baseballs, and the cost of a case of golf balls.
7oj
Use matrices to solve the following systems of equations.
x+y:z x+q-ÿ :O
! sy-2z: 4 Sÿ-2ÿ :'t"
5x ++y
2y +
3z = -15
, .ÿ4x
+z=
0
-2x+ sy = 8-2xÿ5ÿ1 =ÿ
6x-5y-5z = 52
X.ÿ 2
-5 -5 52_ÿ
Defin...___ee the variables. Write the system of equations. Solve the system using matrices.
q, !A hair salon receives a shipment of 84 bottles of hair conditioner to use and sell to customers.
The two types of conditioners received are type A, which is used for regular hair, and type B, which
is used for dry hair. Type A costs ÿ6.50 per bottle and type B costs ÿ;8.25 per bottle. The hair salon's
• H+ow many of each type of conditioner are in the shipment?
6,50a+g.!Sb-511 k6.1o 1.2s
/
01, 1 You have ÿ123.50 in quarters and dimes. There are 1202 coins altogether• Find out how many of
, A box of wood pieces contains wood cut into triangular, square, and pentagonal shapes. There are
80 pieces of wood in the box, and the pieces have a total of 292 sides. If there are 16 more square
es, find the number of pieces of wood of each shape in the box.
t=+riar ular--
t a -p
S-p:lÿ
lz
,
Lÿ. ° ! Alex purchased a pair of earrings, a necklace, and 2 bracelets for $77.50. Her sister purchased three pairs of
earrings, a necklace, and a bracelet for $70.00. The bracelet cost three times as much as the earrings. Find the cost
of a pair of earrings, the cost of a necklace, and the cost of a bracelet.
e:e_Amhÿs= ÿ 7.50
3ÿ+1 n +
b, bracdet zt.ÿ
b
o I
), j A stadium has 49,000 seats. Seats sell for $25 in Section A, $20 in Section B, and $15 in section C.
The number of seats in Section A equals the total number of seats in Sections B and C together. If
kes in S1,052,000 from each sold-out event, how many seats does each section hold?
b.; Sÿdÿ 8: lqÿ ÿqts! 2r,ÿ÷ ÿb tÿ -lj{)ÿ2,ÿsL'z5 2o Is Ij6§2,1]ÿ)
0.--b-c : O
" i A plane travels 896 miles in 3.2 hours with a tail Wind. It then travels 732 miles in 3 hours with a head wind.
: Find the_sspeed of the plane (with no wind) and
-
-
qÿ° ÿ.ÿtÿ.ÿ=ÿ ÿÿ
LÿFM ÿÿ r._ÿthe wind speed'
|5° 'During a home volleyball tournament, high school students sell snacks. They sell cold sandwiches
for $2.50, hot dogs for $1.50, and hamburgers for $2. By the end of the day, the students have
collected $1060.50 and sold 562 items. Allison estimates that the students sold twice as many hot
dogs as cold sandwiches. If her estimate is correct, how many of each item did the, sell?
¢+h÷b -562-
a=ho+doq b - burflÿr : Iÿ1
-I 1
2.50c t 1.5o h t:2.b = lOtÿO.5o 2.ÿ
h:2c
___J
1 5tÿ2 _ ]
t,ÿl::>
-ÿ-
I
2 10¢<).
0
0
- h
I
jÿ, For a fundraiser, Grace sold 2 coupon books, a tub of cookie dough, and a keychain and collected $67.50. Joyce
collected $70.00 and sold 2 coupon books and 2 tubs of cookie dough. Marcy sold the same amount as Joyce plus a
keychain and collected $77.50. Find the cost of a coupon book, the cost of a tub of cookie dough, and the cost of a
keychain.
: ¢outÿ0ÿ kÿ = ,ÿ ;5.00
2c$ ld ,1t< = 87.ÿ0
2c +2d +OE =70.ÿ
2c4-2d+1 k: : 77,58
t 1 ÿ7.50
20 70.ÿ
2 I 77.5/)
7.
The tables below show some values that satisfy two linear equations, respectively.
Equation 1
-k\
Equation 2
x
y
-14
5.3
-12 5.9 +.{o
What is the solution to the system of equations?
-10
6.5
-8
7.1
-6
7.7
-4
8.3
-2
8.9
C x=9, y=12.2
0
9.5
D x=12, y=16.7
2
10.t
4
10.7
A x=6, y=ll.3.