For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book? In this problem, you are asked to find the price of the first book Jane purchased.
For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don’t know the price of the first book.
For example, assign the variable x{\displaystyle x} to the unknown in the problem, which is the price of the first book. Write x=the price of the first book{\displaystyle x={\text{the price of the first book}}}.
Multiplication keywords include times, of, and factor. [9] X Research source Division keywords include per, out of, and percent. [10] X Research source Addition keywords include some, more, and together. [11] X Research source Subtraction keywords include difference, fewer, and decreased. [12] X Research source
For example, you know that the second book is $80, and you know what $80 equals in terms of the price of the first book (x{\displaystyle x}). So set 80 equal to $10 less (−10{\displaystyle -10} ) than 3 times the price of the first book (3x{\displaystyle 3x}). Putting everything together, you have 80=3x−10{\displaystyle 80=3x-10}.
Use inverse operations to isolate a variable. For example, to isolate the variable in the equation 80=3x−10{\displaystyle 80=3x-10}, you need to add 10 to both sides, then divide by 3:80=3x−10{\displaystyle 80=3x-10}80+10=3x−10+10{\displaystyle 80+10=3x-10+10}90=3x{\displaystyle 90=3x}903=3x3{\displaystyle {\frac {90}{3}}={\frac {3x}{3}}}30=x{\displaystyle 30=x}
When combining like terms, remember that only terms with the same exponent and variable can be combined. For example, 4x{\displaystyle 4x} and 2x{\displaystyle 2x} can be combined, 3x2{\displaystyle 3x^{2}} and 5x2{\displaystyle 5x^{2}} can be combined, and 8xy{\displaystyle 8xy} and 4xy{\displaystyle 4xy} can be combined.
For example, since x=the price of the first book{\displaystyle x={\text{the price of the first book}}}, and 30=x{\displaystyle 30=x}, you know that the price of the first book Jane bought was $30.
Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
Since you are combining their profits and tips, you will be adding two terms. So, x = __ + __. The first term will be equal to their profits. Since they make $0. 75 for every cup of lemonade they sell, their profits are equal to . 75c{\displaystyle . 75c}. So, x=. 75c+??{\displaystyle x=. 75c;+;??}. The second term will be equal to their tips. Since their parents are doubling their tips, their tips will be equal to 2t{\displaystyle 2t}. So, x=. 75c+2t{\displaystyle x=. 75c+2t}. Since the variable you are describing is already isolated, and all like terms are combined, you have arrived at your final answer.
