NAME
3-1
DATE
PERIOD
Word Problem Practice
Solving Systems of Equations
4. GAMES Mark and Stephanie are
playing darts according to World Darts
Federation rules. Each toss earns points
depending on where the dart lands. Each
ring and sector is worth a different
number of points. Mark and Stephanie
both toss three darts in the first round. It
happens that their darts only land in two
areas of the board.
y
12
5 20 1
18
4
9
5
13
14
6
11
Ship B
5
O
7
a. Stephanie earned a total of 60 points
with two darts landing in the first
area and one dart landing in the
second area. One of Mark’s darts
landed in the first area and two in the
second. He scored 75 points. Write a
system of equations for their scores.
Use x for the first area and y for the
second area.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(5, 10)
2. LASERS A machine heats up a single
point by shining several lasers at it. The
equations y = x + 1 and y = -x + 7
describe two of the laser beams. Graph
both of these lines to find the coordinates
of the heated point.
2x + y = 60; x + 2y = 75
y
b. Solve the equations. How many points
is the first area worth?
How many points is the second
area worth?
5
O
2
19 3 17
x
Ship A
x = 15; y = 30
5
c. If Mark and Stephanie are playing to
150 points and their darts continue to
land in only the two areas, which
different combinations of darts
landing in the two areas will add up to
150? How many darts landing in the
first area would total 150 points? How
many darts landing in the second
area?
x
3. PRICES At a store, toothbrushes cost
x dollars and bars of soap cost y dollars.
One customer bought 2 toothbrushes and
1 bar of soap for $11. Another customer
bought 6 toothbrushes and 5 bars of soap
for $38. Both amounts do not include tax.
Write and solve a system of equations for
x and y.
10 darts in first area; 5 darts in
second area; also 2 darts in first
and 4 in second; 4 darts in first
and 3 in second; 6 darts in first
and 2 in second; 8 darts in first
and 1 in second. 10 darts.
5 darts.
2x + y = 11
6x + 5y = 38
x = 4.25 and y = 2.50
Chapter 3
15
16
-5
(3, 4)
10
8
9
Glencoe Algebra 2
Lesson 3-1
1. SPOTLIGHTS Ship A has coordinates
(-1, -2) and Ship B has coordinates
(-4, 1). Both ships have their spotlights
fixated on the same lifeboat. The light
beam from Ship A travels along the line
y = 2x. The light beam from Ship B
travels along the line y = x + 5. What
are the coordinates of the lifeboat?