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Trig/Math Anal
Q2WS1
3.6 Use Systems to Solve Equations
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Name___________________
Assignment #______
The degree measure of one of two complementary angles is
30 less than twice that of the other. What are the degree
measures of the angles?
The degree measure of one of two supplementary angles is
6 more than one-half that of the other. What are the
degree measures of the angles?
A collection of dimes and quarters has a total value of five
dollars and contains 29 coins. How many of each kind of
coin are there in the collection?
Tickets for a benefit performance of a new movie sold at
$5.50 for the orchestra section and $3.25 for the balcony.
If the receipts from the sale of 1800 tickets totaled
$7110. How many tickets were sold at each price?
A glass manufacturer makes two grades of glass which
differ in silica content. If she has 2400 kilograms of silica
with which to make one batch of each type, and she uses
510 more kilograms of silica for one type than for the
other. How many kilograms of silica are used for each
type?
In five years a boy will be two-thirds as old as his uncle will
be. Three years ago he was half as old as the uncle is now.
How old are the boy and his uncle?
With an 80 km/h head wind, a plane can fly a certain
distance in four hours. Flying in the opposite direction with
the same wind blowing, it can fly that distance in one hour
less. What is the plane’s airspeed?
Traveling downstream, a boat can go 18 km in 2 hours.
2
Going up-stream, it makes only 3 this distance in twice the
time. What is the rate of the boat in still water, and what
is the rate of the current?
15. Find values of A and B so that the line whose equation is
Ax  By  6
will contain the pints whose coordinates
are (6, 8) and (15, -4).
16. Find values for a and b so that the set of ordered pairs
lx, y: y  ax  bq
2
17. If
will contain (2, 3) and (-3, 13).
 x , y : y  mx  b
contains (1, 7) and (-1, 1), find m
and b.
18. If
 x , y : y  mx  b
contains (-4, -1) and (2, -4), find
m and b.
19. Two temperature scales are established, one, the R scale
where water under fixed conditions freezes at 5º and boils
at 405º, and the other, the C scale where water freezes at
0º and boils at 100º. If the R and C scales are linearly
related, find an expression for any temperature R in terms
of a temperature C.
20. The final velocity of a uniformly accelerated particle is
linearly related to the elapsed time by the equation
v  v o  at , where a and v o are constants. If v=15
when t=10, and v=35 when t=25, find values for
a
and
vo .
In problems 21-24, the original number is a positive twodigit integer. In each problem, find this integer.
21. The sum of the numbers named by the digits is 8. When
the digits are interchanged, the resulting numeral names a
new number that exceeds the original number by 18.
22. The sum of the numbers named by the digits is 10. The
original number is 2 less than three times the number
represented when the order of the digits is reversed.
23. The number named by the units digit is 1 more than twice
the number named by the tens digit. The number
represented when the order of the digits is reversed is 7
less than 8 times the sum of the numbers named by the
digits.
24. The number named by the tens digit is 5 more than the
number named by the units digit. If the digits are
interchanged and the number represented by the resulting
numeral is added to the original number, the sum is 143.
25. A river steamer travels 48 km downstream in the same
time that it travels 32 km upstream. The steamer’s
engines drive in still water at a rate that is 16 km/h
greater than the rate of the current. Find the rate of the
current.
26. Jean finds that in still water her outboard can drive her
boat 3 times as fast as the rate of the current in Pony
River. A 16 km trip up the river and back requires 4 hours.
Find the rate of the current.
27. Two railroad workers are together in a 1.2 km mountain
tunnel. One walks east and the other west in order to be
out of the tunnel before the Bad Creek Express comes
through at 60 km/h. Each man reaches his respective end
of the tunnel in 6 minutes. If the man walking east reaches
the east entrance just before the train enters, and the
train passes the other man 0.24 km beyond the west end of
the tunnel, at what rate did each man walk?
28. Two kilometers upstream from his starting point, a rower
passed a log floating with the current. After rowing
upstream for one more hour, he rowed back and reached
his starting point just as the log arrived. How fast was the
current flowing?
ANSWERS:
7.
8.
9.
10.
11.
40º, 50º
64º, 116º
15 d, 14 q
560 orch., 1240 bal
1455 kg, 945 kg
12. 17, 28
13. 560 km/h
14. 6 km/h; 3 km/h
15.
1
2
,
3
8
16. y  2 x  5
2
17. y  3x  4
18. y 
1
2
x3
R  4C  5
20. vo  53 ; a 
19.
21. 35
4
3
22.
23.
24.
25.
26.
27.
28.
82
37
94
4 km/h
3 km/h
10 km/h W; 2 km/h E
1 km/hr