Algebraic Translations Topic Index | Algebra Index | Regents Exam Prep Center

In the lesson on Algebraic Representations we looked at writing mathematical expressions.
We are ready now to write mathematical equations.

 Expressions: 10,   2 + y,   z,   7xy,      5x - 6,   2(a + 3),          x2 + 4x + 4   "Expressions" do NOT have an equal sign.
 Equations:                2 + y = 10     5x - 6 = 41        x2 + 4x + 4 = 0        "Equations" have an EQUAL sign.
 "Expressions" and "equations" refer to two different entities in mathematics. If you are dealing with an EQUAL SIGN, you are dealing with an "equation". EQUAtion ↔ EQUAL sign An equation is a sentence where two algebraic expressions are equal.

 Examples

Translate the following problems into equations:
HINT:  If you are having trouble determining what the equation might be, make a numerical problem to see how the numbers in the problem are related to one another.

 1 Cost for cable TV service in a certain city is \$45 for the installation and \$24 a month for service. Number problem:  for 3 months the cost would be:  Cost = \$24 • 3 + \$45.  Replace 3 with m. Let c = cost, m = number of months c = 24m + 45 2 If golf balls cost \$1.25 and putters cost \$79, how many of each can the golf team purchase for \$150? Number problem:  if I purchase 2 golf balls and 3 putters the cost will be:   Cost = 1.25•2 + 79•3 Replace 2 with g (number of golf balls), 3 with  p (number of putters), and Cost with \$150. Let g = number of golf ball,  p = number of putters 1.25g + 79p = 150 3 H2O means that water contains two hydrogen atoms and one oxygen atom. Number problem:  In water, if there is one oxygen atom, there are 2 hydrogen atoms; if there are two oxygen atoms, there are 4 hydrogen atoms and so on.  The number of hydrogen atoms is twice the number of oxygen atoms. Let O = number of oxygen atoms,  H = number of hydrogen atoms H = 2O 4 A cookie recipe calls for twice as many chocolate chips as walnuts. Number problem:  if a recipe calls for 10 walnuts, it calls for 20 chocolate chips.  The number of chocolate chips is twice the number of walnuts. Let c = number of chips,  w = number of walnuts c = 2w 5 What is the total weight of a filled hot tub, if the tub weighs 350 pounds and the water weighs 10 pounds per gallon? Number problem:  if it takes 100 gallons to fill the hot tub, the total weight will be: Total = 10 • 100 + 350  Replace 100 with g, for the number of gallons.. Let t = total weight, g = number of gallons t = 10g + 350

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