Transcript Problem Solving Using Equations

Problem Solving Using
Equations
Math word problems can, in most
instances, be translated in math equations
and quickly solved.
The language of math is similar to any
other language, complete with nouns,
verbs, adjectives, phrases, sentences
etc…
Problem Solving using Equations
A list of some of the symbols, phrases,
and sentences that you will be using are
listed below to assist you in translating
from English to math and vice versa.
Translation
Math
English equivalent
+
Plus, add, increase, greater than, larger,
augment
-
Subtract, minus, negative, decrease,less
than,reduce,diminish
x
Times, of, multiply
÷
Divided, goes into, a certain number of
parts
X,a,q,t,p,y,z,n,d,g,m,etc.
A number, an age, a quantity, a mass, a
volume, a certain amount, etc…
7x
Seven times a number, a number times 7
N+6
A number increased by 6, 6 larger than a
number
T-9
A number decreased by 9, 9 less than a
number, a number reduced by 9
4x+_7=8
4 times a number plus 7 equals 8
(x)(x)
A number times itself
Please Translate Together
3x
(3g)(23)
A number
A number doubled
The square of a number
A number increased by five
The sum of a number and fifteen
One-half of a number plus the number
Six decreased by a number is the number
Five times a number plus eight is eighty-five
Three consecutive numbers
Answers
Three times a number
Three times a number times 23
X , y, r, etc…
2x
X
X+5
X=15
½x+x
6-x=x
5x+8=85
X, x+1, x+2
Try some on your own
A number is doubled the result is twelve
Seven times a number is negative fifty-six
A number plus twice a number plus three times a
number is seventy-five
Six less than triple a number is nine
The product of five more than a number and six is thirty
We get four when we subtract fifteen from twice a
number
The product of two consecutive numbers is fifty-six
Nine times a number plus the number quadrupled is zero
Putting this Together to Solve Word
Problems
Example:
If a number is doubled and the result is
increased by 4, the sum is ninety four. Find the
number.
2x+4= 94
2x + 4-4=94-4
2x=90
2x = 90
2
2
X= 45
Problem Solving (Continued)
The larger of two numbers is seven more than five times the
smaller. Their sum is sixty-one. What are the numbers?
Larger: 5x+7 Smaller: x
5x+7+x=61
5x+x=61-7
6x=54
6x = 54
6
6
X= 9
Therefore the smaller number is 9 and the larger is 52 because
5(9)+7=52 
Still more…
If three is added to a number and the sum is
multiplied by two, the result is the same as nine
subtracted from three times the number. Find
the number.
2(x+3)=3x-9
2x+6=3x-9
2x-3x= -9-6
-1x= - 15
-1x = -15
-1
-1
X=15
Ok, you talked me into one more…
The sum of three consecutive numbers is thirty-three. What are
the numbers?
First: x
Second: x+1
Third: x+2
(x)+(x+1)+(x+2)=33
3x+3=33
3x+3-3=33-3
3x=30
3x = 30
3
3
X= 10
Therefore the 3 consecutive numbers are, 10 + 11 + 12 = 33