Transcript 5.6b Word Problems with Standard Form - PMS-Math
Warm-Up
Write an equation in standard form of the line that passes through the given point and has the given slope
m
or that passes through the two given points.
1.
(-5, -6),
m
= 3
ANSWER
2
x
+
y
= – 4
2.
(– 4, – 3), (1, 6)
ANSWER
– 2
x
+
y
= 5 3. Rewrite the equation in standard form with integer coefficients.
a) 0.5x + 0.38y = 0.2
b) 2.3x + 0.283y = 3.28
5.6b Students will be able to use the standard form of linear equations to solve word problems.
Daily Homework Quiz
For use after Lesson 5.6
Write an equation in standard form of the line that passes through the given point and has the given slope
m
.
1.
(1, – 6),
m
= – 2
ANSWER
2
x
-
y
= – 9 2. Rewrite the equation in standard form with integer coefficients.
3.5x + 0.38y = 38 350x + 38y = 3800 5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem Library Your class is taking a trip to the public library. You can travel in small and large vans. A small van holds
8
people and a large van holds
12
people. Your class could fill
15
small vans and
2
large vans.
a .
Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill.
b .
Graph the equation from part
(
a
)
.
c. List several possible combinations.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem SOLUTION a .
Write a verbal model. Then write an equation.
8
s
+ 12
l
=
p
Because your class could fill
15
small vans and
2
large vans, use
(15, 2)
as the
s
- and
l
-values to substitute in the equation value of
p
.
8
s
+ 12
l
=
p
to find the
8(15) + 12(2) =
p
144 =
p
Substitute
15
for
s
and Simplify.
2
for
l
.
Substitute
144
for
p
in the equation
8
s
+ 12
l
=
p
.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem ANSWER The equation
8
s
+ 12
l
combinations.
= 144
models the possible b. Find the intercepts of the graph .
Substitute
0
for
s
.
8(0) + 12
l
= 144
l
= 12
Substitute
0
for
l
.
8
s
+ 12(0) = 144
s
= 18 5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem Plot the points
(0, 12)
and
(18, 0).
Connect them with a line segment. For this problem only nonnegative whole-number values of
s
and sense.
l
make c.
The graph passes through
(0, 12), (6, 8),(12, 4),
and
(18, 0).
and
12
So, four possible combinations are large
, 6
small and
8
large
, 0
small
12
small and
4
large
, 18
small and
0
large.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
7.
WHAT IF?
In Example 5 , suppose that 8 students decide not to go on the class trip. Write an equation that models the possible combinations of small and large vans that your class could fill. List several possible combinations.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
SOLUTION
STEP
1
Write a verbal model. Then write an equation.
8
s
8
class could fill
14 + 12
l
=
p
students decide not to go on the class trip, so the small vans and
2
large vans. Because your class could fill
14
small vans and
2
large vans, use
(14, 2)
as the
s
- and
l
-values to substitute in the equation
8
s
+ 12
l
=
p
to find the value of
p
.
8(14) + 12(2) =
p
136 =
p
Substitute
14
for
s
and
2
for
l
.
Simplify.
Substitute
136
for
p
in the equation
8
s
+ 12
l
=
p
.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
ANSWER The equation
8
s
combinations.
+ 12
l
= 136
models the possible
STEP
2
Find the intercepts of the graph.
Substitute
0
for
s
.
8(0) + 12
l l
= 136 4 = 11 12
Substitute
0
for
l
.
8
s
+ 12(0) = 136
s
= 17 5.6b Students will be able to use the standard form of linear equations to solve word problems.
GUIDED PRACTICE
for Example 5 Plot the point
(0,11 ) 12
and
(17, 0).
connect them with a line segment. For this problem only negative whole-number values of
s
and
l
make sense.
STEP
3
The graph passes through
(17, 0), (14, 2), (11, 4), (8, 6), (5, 8)
and
(2, 10).
So , several combinations are
17 4
large small
; 18 , 0
large small ,
6 ; 14
small
2
large
; 5
large small,
8 ; 11
large
;
small,
2
small ,
10
large.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
Daily Homework Quiz
For use after Lesson 5.4
3. You have
$96
to spend on campground activities. You can rent a paddleboat for
$8
per hour and a kayak for
$6
per hour. Write an equation in standard form that models the possible hourly combinations of activities you can afford. List three possible combinations .
ANSWER
8
p
+ 6
c
= 96; 16 h
kayak and
0 h
paddleboat;
12 h
paddleboat and
0 h
kayak;
6 h
paddleboat and
8 h
kayak.
5.6b Students will be able to use the standard form of linear equations to solve word problems.