Download A-REI Solve equations and inequalities in one

A-CED Create equations that
describe numbers or relationships.
1. Create equations and inequalities in one variable
and use them to solve problems. Include equations
arising from linear and quadratic functions, and
simple rational and exponential functions.
Ratio Problem
The ratio of girls to boys in Mrs. Franks’
Algebra class is 3:4 (excluding Mrs. Franks).
On Monday, 4 girls and 6 boys got to go on a
special field trip for honor roll students.
Since no other students were absent on
Monday, the ratio of girls remaining in the
class to boys remaining in the class was 4:5.
How many students are in Mrs. Franks’ class
when everyone is present?
Understanding the Problem
The ratio of girls to boys in Mrs. Franks’ Algebra class is 3:4
(excluding Mrs. Franks). On Monday, 4 girls and 6 boys got to
go on a special field trip for honor roll students. Since no other
students were absent on Monday, the ratio of girls remaining
in the class to boys remaining in the class was 4:5.
How many students are in Mrs. Franks’ class when everyone is
present?
Guess, Check and Revise
On Monday, 4 girls and 6 boys got to go on a
special field trip for honor roll students.
If you there are only 3 girls and 4 boys in the class,
there aren’t enough to send 4 girls and 6 boys on the
fieldtrip.
Guess, Check and Revise
Lets try adding in 3 more girls and 4 more boys
to maintain the 3:4 ratio.
Now we have 6 girls and 8 boys in the class.
Guess, Check and Revise
On Monday, 4 girls and 6 boys got to go on a
special field trip for honor roll students.
Guess, Check and Revise
On Monday, 4 girls and 6 boys got to go on a
special field trip for honor roll students.
Now, there are 2 girls
and 2 boys remaining
in the class which is a
1:1 ratio.
We need to find a 4:5
ratio for the
remaining students.
Repeat this approach until
the remaining students
are in the 4:5 ratio of
girls to boys.
Write an Equation
The ratio of girls to boys in Mrs. Franks’
Algebra class is 3:4 (excluding Mrs. Franks).
If the ratio of girls to boys in the
class is 3:4,
Then…
The number of girls in the class =
3x
The number of boys in the class = 4x
Where x the common factor needed to maintain the ratio
Write an Equation
On Monday, 4 girls and 6 boys got to go on
a special field trip for honor roll students.
If the # of girls in the class is 3x and
The # of boys in the class is 4x,
Then…
The number of girls remaining in class =
3x - 4
The number of boys remaining in class =
4x - 6
Write an Equation
Since no other students were absent on
Monday, the ratio of girls remaining in the
class to boys remaining in the class was 4:5
If the number of girls remaining in class = 3x - 4
and the number of boys remaining in class = 4x - 6
Then…
3x - 4 4
=
4x - 6 5
Solve the Equation
The ratio of girls to boys in
Mrs. Franks’ Algebra class is
3:4 (excluding Mrs. Franks).
On Monday, 4 girls and 6 boys
got to go on a special field trip
for honor roll students. Since
no other students were absent
on Monday, the ratio of girls
remaining in the class to boys
remaining in the class was 4:5.
How many students are in
Mrs. Franks’ class when
everyone is present?
3x - 4 4
=
4x - 6 5
5 (3x - 4) = 4 ( 4x - 6)
15x - 20 =16x - 24
x=4
Is 4 the solution
to this problem?
Answer the problem
How many students are in Mrs. Franks’ class
when everyone is present?
If the common factor is
x=4
Then…
The number of girls in the class = 3( 4) =12
The number of boys in the class = 4 ( 4) =16
Therefore, there are 28 students in Mrs. Frank’s class.
Check the answer
If there are 12 girls and 16 boys in the class,
This is a total 28 students. The ratio of girls to boys
is 12 :16 which is equivelent to 3 : 4.
If 4 girls and 6 boys go on the trip, there will be
8 girls and 10 boys remaining in the class. 8 :10 is
equivilant to 4 : 5.