Pick a Ride
Differentiated Problems for
Multi-Step Equations
Pick a Ride (Roller Coaster)
Pick the ride you are most comfortable with…
“Dahlonega Mine
Train”
a small roller coaster
and easy ride . . .
Pick a Ride
Pick the ride you are most comfortable with…
“Great American
Scream Machine”
A little more excitement
and thrills . . .
Pick a Ride
Pick the ride you are most comfortable with…
“Goliath”
Fast moving and breathtaking ride . . .
Pick a ride …

3(b  7)  30
4( q  2)  4  8
( x  10)  7
b3
q3
x3
Pick a ride …

5  6 a  5  a
a  2
3(b  9)  6
b  7
6
1
 4( n  1)
2
n
5
8
Pick a ride …

5 x  1  x  11 15a  10  9a  2 12x  12  4x  14  14
x2
a 
1
2
x  5
Pick a ride …

x  (12  x)  38 12.5  2 g  3.5
x  25
g 8
6.5  2.5r 11
r 7
Pick a ride …

3 y  5 y  64 2a  a  10  5 6  y  3  3 y  17
y 8
a 5
y2
Pick a ride …

3(b  9)  6 30  5(6n  6) 8c  4(c  8)  8
b  7
n  2
c  10
Pick a ride …

35  7x 10x  22 9  48  10a  2a  9 8x  3x 10  20
x  19
a6
x6
Pick a ride …

(r  8)  14 12  4(6 x  3) 5x  3(6 x  7)  177
r  6
x0
x  12
Pick a ride …

11w  9  7w  15 12n 14 10n  80
w  12
n3
2  3 y  18  5 y
y  8
Pick a ride …

( x  3)  15
3  4( z  5)  31
x  12
z  2
3  12 y  5(2 y  7)
y  19
Pick a ride …

x  3x  20  40 6 y  2 y  8  48 4x  5 14x  83  7
x  15
y  6
x5
Pick a ride …

2(r  7)  40 5m  2(m  1)  23 5 x  4(3x  4)  186
r  13
m3
x  10
Pick a ride …

4d  2  d  23 9  7z 13z  21 36  4b  3b  2 18 12
d  7
z  5
b4
Pick a ride …
A1 Plumbing Service
charges $35 per hour plus
$25 for a service call.
Good Guys Plumbing
Repair charges $40 for a
service call with no travel
charge. How long must a
service call be for the two
companies to charge the
same amount?
t = # hours
35t + 25 = 40t
t = 5 hours

Mike’s Fitness Center
charges $30 per month for
a membership. All-Day
Fitness Club charges $22
per month plus an $80
initiation fee for a
membership. After how
many months will the total
amount paid to the two
fitness clubs be the
same?
t = # months
30t = 22t + 80
t = 10 months
Pick a ride …
The Lone Star Shipping
Company charges $14 plus
$2 a pound to ship an
overnight package.
Discount Shipping
Company charges $20 plus
$1.50 a pound to ship an 
overnight package. For
what weight is the charge
the same for the two
companies?
x = # of pounds
14 + 2x = 20 + 1.50x
x = 12 lb.
Deanna and Lise are
playing games at the
arcade. Deanna started
with $15 and the machine
she is playing costs $0.75
per game. Lise started
with $13 and her machine
costs $0.50 per game.
After how many games
will the 2 girls have the
same amount of money
remaining?
x = # of games
15 – 0.75x = 13 – 0.50x
x = 8 games
Pick a ride …
The Wayside Hotel charges
its guests $1 plus $0.80 per
minute for long distance
calls. Across the street,
the Blue Sky Hotel charges
its guests $2 plus $0.75 per
minute for long distance 
calls. Find the length of a
call for which the 2 hotels
charge the same amount.
x = # of minutes
1 + 0.80x = 2 + 0.75x
x = 20 minutes
Duke and Kila are
students at Horizon
Community College.
Duke currently has 22
credits and he plans to
take 6 credits per
semester. Kila has 4
credits and plans to take
12 credits per semester.
After how many
semesters will Duke and
Kila have the same
number of credits?
x = # of semesters
6x + 22 = 12x + 4
x = 3 semesters