Lesson 4-3: Word Problems

1
Lesson 4-3 Word Problems

• Objective
• Students will
• Use systems of equations to model and solve word
  problems

2
Translate to a system then solve Example 1 Twice
a number added to a 2nd number is
eleven. Twice the second number, added to
the first number, equals 1. Find the
numbers? Ist number x 2nd numbery Ist
equation 2x y 11 2nd equation 2y x
1
Which method do you like here? Solve!!
3
Mixture- Fill in the following table for all
mixture problems
x
Amount Amount in solution
A
B
(AB) total

4

• Example 2 30 fat cream is mixed with 2 fat
  milk to make 100 gallons of milk that is 4 fat.
  How much of cream and 2 milk should be used?

Amount Amount in solution
A (cream)
B (milk)
(AB) total
x

x

0.3x
0.30
x
x

0.02
y
0.02y
x

0.04
100
4
x y 100 0.3x 0.02y 4
Now pick a method and solve
5

• Distance D rt
• Complete the following table to help understand
  the relationship
• All distance problems ? Find a relationship
  between A and B
• Possible when distance is missing
• d1d2 (when will they meet)
• d1 d2 dtotal (opposite directions or toward
  each other)
• d1-d2 dapart (when will they be certain
  distance apart)

x
r t d
A
B

6

• Example 3
• Agnes walks at 3 mph. Four hours later Fred
  bikes at 15 mph to catch her. How long until
  Fred catches her?

r t d
Agnes
Fred
x

x

da
3
t
x

df
15
t - 4
They will have went an equal distance when Fred
catches her so this is a dagnes dfred
equation Using substitution we get 3t
15(t-4) 3t 15t -60 60 12t 5
t, since t was for Agnes, Fred went t - 4 (5-4)
or 1 hour!!!
7
Age x age now y 2nd age now 3 years from
now 5 years ago x 3 x 5 y 3 y
5
8

• Example Fred is 8 years older than his sister.
  4 years ago his sister was 2/3 as old as Fred.
  How old are they now?
• Fred f
• Sister s
• Translate
• Sentence 1 f s 8
• Sentence 2

Substitution seems the right choice here!
Now solve!! Dont forget Fred!!!!!