How do you use distributive property to solve word problems?

The distributive property states that a*(x+y)=a*x+a*y. The distributive property can be applied when the same operation is being done to multiple terms in an expression. Distributing out the coefficients in a word problem can make it easier to manipulate and isolate the variables in word problems.

1. Find numbers, operations and relationships

   Read the word problem. Look for any numbers and how they relate to each other. Find comparative phrases, such as "3 more than" or "15% less than," to determine the operation that creates the relationship. Write these relationships as equations. For example, a word problem might say that a father purchased five ice cream cones for a total of $32, four of which were served with a second scoop that cost $3 more than the regular price he paid for the fifth. The number 32 is the total and is made up of a combination of one cone at regular price and four cones at a price $3 higher. Where c is a regular cone and d is a double, c+3=d and 4d+c=32.

2. Use substitution to make all of the variables the same

   In the example above, because c+3=d, c can be substituted for d:

   4d+c=

   4(c+3)+c=32.

3. Use distribution and isolate the variable

   In the example above, the coefficient 4 can be distributed:

   4(c+3)+c=

   4(c)+4(3)+c=

   4c+12+c=

   5c+12

   To isolate the variable, subtract constants, then divide out the coefficients:

   5c+12=32

   5c+12-12=32-12

   5c=20

   5c/5=20/5

   c=4

   Check your answer by plugging the variable back in.