Solving Word Problems with Variables on Both Sides
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Transcript Solving Word Problems with Variables on Both Sides
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.