Solving Word Problems with Variables on Both Sides

SOLVING WORD PROBLEMS
WITH VARIABLES ON BOTH
SIDES

Peter and Maggie each opened savings accounts on
the same day, intending to withdraw the money for
weekly expenses. Peter opened his account with
\$710 and withdrew \$35 per week. Maggie
opened her account with \$570 and withdrew \$25
weekly. In how many weeks will their accounts be
equal.

Peter and Maggie each opened savings accounts on the same day, intending to
withdraw the money for weekly expenses. Peter opened his account with \$710 and
withdrew \$35 per week. Maggie opened her account with \$570 and withdrew
\$25 weekly. In how many weeks will their accounts be equal.

710
- 35W = 570 - 25W

(-570) + 35W =(-570) + 35W

140
=
10W

/10
=
/10

14 WEEKS

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?






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?
90 + 9y = 50 + 13y
(-50) - 9y = (-50) - 9y
40
=
4y
/4
=
/4
10 sq. yards of carpeting

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?






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 IF THE CAR IS
RENTED FOR ONLY ONE DAY?
44 + .06m = 35 + .09m
(-35) - .06m = (-35) - .06m
9
=
.03m
/.03
/.03
300 MILES

Nancy has \$250 in her savings account. She plans
to save \$15 per week from her salary. Caty 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?

Nancy has \$250 in her savings account. She plans to save \$15 per week from her
salary. Caty 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?






250 + 15w = 200 + 20w
(-200) - 15w = (-200) - 15w
50
=
5w
/5
/5
10 WEEKS

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?






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?
250 + 25s
- 25s
250
/25
10 STEREOS
= 50s
= -25s
= 25s
= /25