# IS LESS THAN - hollyphelps

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```Ch 7 – The Basic Concepts of Algebra
7.2 – Applications of Linear
Equations
VERBAL
SUM of a number and 3
4 MORE THAN a
number
A number PLUS 9
A number INCREASED
BY 3
MATHEMATICAL
x+3
x+4
x+9
x+2
x+3
Synonyms for SUBTRACTION:
VERBAL
DIFFERENCE of a
number and 3
4 LESS THAN a number
A number MINUS 9
A number
DECREASED BY 3
MATHEMATICAL
x–3
x–4
x–9
x–3
Synonyms for MULTIPLICATION:
VERBAL
PRODUCT of a number
and 3
4 TIMES a number
2/3 OF a number
24% OF a number
TWICE a number
MATHEMATICAL
3x
4x
2/3x
.24x
2x
Synonyms for DIVISION:
VERBAL
QUOTIENT of a
number and 3
4 DIVDED BY a
number
The RATIO of 8 and a
number
MATHEMATICAL
x/3
4/x
8/x
Synonyms for “EQUAL”:
VERBAL
3 plus a number IS 10
4 minus a number IS
GREATER THAN 8
The product of 5 and a
number IS LESS THAN
100
MATHEMATICAL
3 + x = 10
4–x>8
5x < 100
Let’s try writing verbal phrases as
mathematical expressions!
1. The product of a number and 12 is
decreased by 7.
2.
The sum of a number and 2 is multiplied by
5.
Let’s try writing verbal phrases as
mathematical expressions!
3. The quotient of a number and 3 is 30.
4.
Twice the difference of 12 and a number is
less than 142.
What is the difference of the phrases below?
Write a mathematical model for each.
7 less than a number is 9.
2. 7 and the sum of a number is less than 9
1.
NBA Record
In 2004 – 2005 NBA regular season, the Phoenix Suns
won two more than three times as many games as
they lost. The Suns played 82 games. How many wins
and losses did the team have?
U.S. Senate
During the 109th Congress (2005 – 2006), the U.S.
Senate had a total of 99 Democrats and Republicans.
There were 11 more Republicans than Democrats.
How many Democrats and Republicans were there in
the Senate?
Chemical Mixture
How much pure acid is in 250 milliliters of a 14% acid
solution?
Interest Earned
I = Prt
 If \$10,000 is invested for one year at a 3.5% simple
interest, how much interest is earned? How much
money do you have total?
 If \$550 is invested at a simple interest rate of 4%,
how long would you have to keep your money in the
bank until you have earned \$264 in interest?
In a chemistry class, 12 liters of a 12% alcohol solution
must be mixed with a 20% solution to get a 14%
solution. How many liters of the 20% solution are
needed?
A chemist must mix 8 liters of a 40% acid solution
with some 70% acid solution to obtain a 50%
solution. How much of the 70% solution is needed?
Coin Mixture
A box of coins currently has 44 coins, consisting of
pennies, dimes and quarters. The number of pennies
is equal to the number of dimes. The total value in the
box is \$4.37. How many of each denomination are in
the box?
Distance between Cities
A driver averaged 53 miles per hour and took 10 hours
to travel from Memphis to Chicago. What is the
distance between Memphis to Chicago?
Attendance at a School Play
The school production of Hamlet was a big success. For
opening night, 410 tickets were sold. Students paid
\$3 each and nonstudents paid \$7 each. If a total of
\$1650 was collected, how many students and how
many nonstudents attended?
Movie Ticket Prices
A movie theater has two ticket prices: \$8 for adults and
\$5 for children. If the box office took in \$4116 from
the sale of 600 tickets, how many tickets of each kind
were sold?
2004 Olympic Results
Joanna Hayes of USA ran the 100-m hurdles in 12.37
seconds. What was her rate?
Jeremy Warner of USA ran the 400-m run in 44.00
seconds. What was his rate?
Partner Activity
 Each group will make up a word problem about the
following topics/formulas.
 d = rt
 I = Prt
 A problem with 2 unknowns (i.e. the
Democrat/Republican problem from yesterday or the
Movie Ticket prices today) – NO,YOU CAN NOT USE
ANY OF THE SAME SINARIOS DONE IN CLASS!
 You must write out the problem and provide a
correct solution.
 My favorite ones will be used on the quiz next week!
```