J EvansC Logan 54B Applying Systems Of Linear Equations Define Variables Let x the width Let y the length Equations Which method of solving systems of equations would be best to ID: 580482
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Slide1
Algebra 1 Glencoe McGraw-Hill J. Evans/C. Logan
5.4B
Applying Systems
Of Linear EquationsSlide2
Define Variables:
Let
x
=
the width Let y = the length
Equations:
Which method of solving systems of equations would be best to use?
substitution
1. The length of a rectangle is 2 m more than twice the width. The perimeter is 82 m. Find the dimensions of the rectangle.
The width is 13 m
and the length is 28 m.Slide3
Let g =
# of girls Let
b
= # of boys
Verbal
Model:
2 X # of girls = 3 X # of boys
# girls + # boys = total
Equations:
Which method of solving systems of equations would you use here?
substitution
2. The eighth grade class
at
LCMS has
335 students. Twice the number of girls is equal to three times the number of boys. How many boys and how many girls are in the class?
Define Variables:Slide4
Verbal Model
:
3 X
envelope cost
+ 4 X
paper cost = $13.25
2 X envelope cost + 6 X paper cost = $17.00
Equations:
Which method of solving systems of equations would you use here?
Let
e
= cost of envelopes
Let n = cost of note paper
combinations/elimination
3. The cost of 3 boxes of envelopes and 4 boxes of note paper is $13.25. Two boxes of envelopes and 6 boxes of note paper cost $17. Find the cost of each box of envelopes and each box of note paper.
Define Variables:Slide5
Verbal Model:
amt. of prunes
+
amt.
of apricots = Total amt.
prunes value + apricots value =
mix value Equations:
Which method of solving systems of equations would you use here?
Let p= amount of prunes Let a = amount of apricots
substitution
4. Twenty pounds of dried fruit mix contained prunes worth $2.90 a pound and apricots worth $3.15 a pound. How many pounds of each did the mix contain if the total value of the mix was $59.75?
Define Variables:Slide6
Verbal Model:
$
at 8%
+ $
at 12%
= total $
interest interestfrom 8% + from 12% = total interest account account
Equations:
Which method of solving systems of equations would you use here?
Let
x
= amount invested at 8%; Let
y = amount invested at 12%
substitution
5
.
Mr. Scott kept part of his $5000 savings in an account that earned 8% interest and the rest in an account that earned 12% interest. How much did he have in each account if his annual interest income from the total investment was $514.80?
Define Variables:Slide7
6. The sum of two numbers is 100. Five times the smaller number is 8 more than the larger number. What are the two numbers?
Try this one on your own:
The numbers are 18 and 82.Slide8
#2. Solve
the second equation for g.
You’ve found the number of boys at the school. Use that information to determine the number of girls.
There are 134 boys and 201 girls at the school.Slide9
If boxes of note paper cost $2.45 each, how much do boxes of envelopes cost?
Note paper costs $2.45 and envelopes cost $1.15.
#3. What
could you multiply each equation by to eliminate one of the variables?Slide10
#4. Solve
the first equation for one of its variables.
There were 7 lb. of apricots and 13 lb. of prunes in the mix.
If the mix contained 7 lb. of apricots, how many pounds of prunes did it contain?Slide11
#5. Solve
the first equation for one of its variables.
He had $2130 invested at 8% and $2870 invested at 12%.
If Mr. Scott had $2130 in the 8% account, how much was in the 12% account?