Section 1.3
Modeling with Linear Equations
1. A problem will appear on the screen.
2. Use discussion in your group and paper to solve the
problem.
3. You have three minutes maximum to solve the problem.
4. When you have your answer, write it down on the white
board and hold it up so the teacher can see.
5. First group to get a correct answer gets three points.
6. Second group to get a correct answer gets two points.
7. Any other group who gets a correct answer gets one
point.
8. ONLY ONE ANSWER MAY BE SUBMITTED PER
QUESTION.
9. The group with the most points at 9:45 gets 5 points
extra credit per person, second place 4 points per
person, etc.
The sum of three consecutive numbers is 804.
Find the numbers.
x   x  1   x  2   804
3x  3  804
x  267
267,268,269
70 is 40% of what number?
0.4x  70
x  175
Your paycheck is 15% less than your coworkers.
Your two paychecks total $1391.20. Find the
amount of YOUR paycheck.
x  0.85x  1391.20
x  752
Yours : 0.85x  $639.20
A picture frame has a total perimeter of 48.6 inches.
The height of the frame is 0.62 times its width. Find
the height (h) and the width (w) of the frame. Note,
your answer should look like h = ___ and w = ___
2h  2w  48.6
2  0.62w   2w  48.6
w  15
h  9.3
Two cars start at a given point and travel in the same
direction at average speeds of 40 mph and 55 mph.
How many MINUTES elapse before the two cars are
five miles apart?
55t  40t  5
15t  5
1
t  hr
3
20 minutes
A LWE bus driver traveled at an average speed of 55 mph on
a 200 miles trip to U of I to pick up students. Since I-57 was
closed on the way back, he could only average 40 mph on the
return trip. Find the average speed for the round trip. Round
your answer to the nearest whole number.
55t  200
t
40t  200
40
11
t5
 40


5
 11
 t  400


t  46
To obtain the height of a tree, you measure the tree’s
shadow and find that it is 8 feet long. You also
measure the shadow of a 2 foot lamp post and find
that it is 9 INCHES long. How many feet tall is the
tree?
9 / 12 2

8
x
x9
An apple store has $20,000 of inventory in ipods and iphones.
The profit on an ipod is 25% and the profit on an iphone is
17%. The profit for the entire inventory is 20%. How much
money was originally invested in each? Your answer should
read
Ipods - $_________
Iphones $___________
0.25x  0.17  20000  x   20000 0.20 
Ipods  $7500
0.08x  600
x  7500
Iphones  $12500
Simplify the expression below
5x  25x 
4
5x 4
x2

2
25x
5
2
1
A rectangular kiddie pool is 12 feet long, 3 feet deep,
and 3 feet wide. If 1 gallon = 0.13368 cubic foot, find
the depth of the water when the pool contains 70
gallons of water. Round your answer to TWO
DECIMAL PLACES.
70 gallons  9.3576 cubic feet
12  3  h  9.3576
h  0.26
Solve the equation below for b, writing your answer as
a single simplifed fraction:
1
A  a  b h
2
2A  ah  bh
2A  ah  bh
2A  ah
b
h
Solve the equation below for r, writing your answer as
a single simplifed fraction:
1 2
V  h  3r  h 
3
3V  h2  3r  h 
3V  3h2r  h3
3V  h3
r
2
3h