SOLVING WORD PROBLEMS
WITH VARIABLES ON BOTH
SIDES


Pedro and Maria each opened savings accounts on
the same day, intending to withdraw the money for
weekly expenses. Pedro opened his account with
$710 and withdrew $35 per week. Maria opened
her account with $570 and withdrew $25 weekly.
In how many weeks will their accounts be equal.
The first sentence doesn’t have any relevant
information, so cross it out.



Pedro opened his account with $710 and withdrew
$35 per week. Maria opened her account with
$570 and withdrew $25 weekly. In how many
weeks will their accounts be equal.
What is the question asking for?
If we don’t know something what do we call it?




Pedro opened his account with $710 and withdrew
$35 per week. Maria opened her account with
$570 and withdrew $25 weekly. In how many
weeks will their accounts be equal.
What numbers go with x (weeks)?
We have two numbers that go with x, therefore we
have two equations.
When we have 2 equations we set them equal to
each other



Pedro opened his account with $710 and withdrew
$35 per week. Maria opened her account with
$570 and withdrew $25 weekly. In how many
weeks will their accounts be equal.
The question asks when they will be equal, so we
use an equals sign
Replace the first m with $35 and the second m with
$25



Pedro opened his account with $710 and withdrew
$35 per week. Maria opened her account with
$570 and withdrew $25 weekly. In how many
weeks will their accounts be equal.
They are both taking money away from their
account, so both values of m have to be negative
We then replace the b on Pedro’s equation with
$710 and Maria’s with $570




We now have an equation we can solve for!
Add 35x to both sides
Subtract 570 from both sides
Divide by 10


Pedro and Maria each opened savings accounts on
the same day, intending to withdraw the money for
weekly expenses. Pedro opened his account with
$710 and withdrew $35 per week. Maria opened
her account with $570 and withdrew $25 weekly.
In how many weeks will their accounts be equal.
x = weeks, so in 14 weeks their accounts will be
equal

The Magic Carpet charges $90 for installation and
$9 per square yard of carpeting. The Carpeteria’s
installation price is $50 but the store charges $13
for each square yard. For what number of square
yards of carpeting will the cost, including
installation, be the same for both stores?

Prestige Car Rentals charges $44 per day plus 6¢
per mile to rent a mid-sized vehicle. Gateway Auto
charges $35 per day plus 9¢ per mile for the same
car. For what number of miles will both companies
charge the same price?

Nilda has $250 in her savings account. She plans
to save $15 per week from her salary. Iona has
only $200 in her account but can save $20 a week
from her paycheck. How many weeks will it take
before the amount in each savings account is the
same?

A sales person in a stereo store is given a choice of
two different compensation plans. One plan offers
a weekly salary of $250 plus a commission of $25
for each stereo sold. The other plan offers no
salary but pays $50 commission on each stereo
sold. How many stereos must the sales person sell
to make the same amount of money under both
plans.