[MUSIC] Sometimes we need to solve word problems. In these cases it is very important to properly translate the words expressions into mathematical expressions. For example, let's see how to write the following verbal expressions as mathematical expressions by using x to represent the unknown quantity. Notice that, other letters can also be used in order to represent this unknown quantity. We need write 3 plus a number, this means 3+x. Where x represents the number and the word plus indicates addition. If we say add 3 to a number, this means x+3, where x represents the number and the word add indicates addition. If we need to write the sum of a number and 9, this means x + 9, where x represent the number and there were some indicates addition. If we say 2 more than a number, this means x + 2. Where x represents the number and more than indicates addition. Let's see another example of translating verbal expressions into mathematical expression by using p as a variable If we need to write 2 less than a number, this means p- 2. Where p represents the number and less than indicates subtraction. If we need to write a number decreased by 17, this means p-17, where p represents the number and decreased by indicates subtraction. If we need to write 7 fewer than p, this means p- 7, where p represents the number and fewer than indicates subtraction. Another example of translating variable expression to mathematical expression, by using y as the variable is the product of a number and 3, which means 3y, where y represents the number and the word product indicates multiplication. 4 times a number Means 4y where y represents the number the word times indicates multiplication. 2/3 of a number, it means 2/3y where y represents the number and 2/3 of indicates multiplication. The quotient of a number and 2, it's y/2, where y represents the number and the word quotient, indicates division. The sum of 4 in a number, is multiplied by 7, it means 7(4+y). In this case, we need to include the (4+y). 7 is multiplied by the difference of an unknown number and 18, which means 7(y- 18). Also in this case we need to include (y- 18). Let's look at another example and translate. The product of 5 and a number increased by 8 is 100, into an equation. Then, let's solve the equation. Let us use the letter y as the variable and translate as follow. 5 x (y + 8)=100. Now, we need to solve our equation. We need first to simplify, and after complete the solution of the equation. So first of all we get 5y plus 40, which is 5 times y plus 5 times 8 equal to 100. And after, we can solve the equation by subtracting 40 from both sides of the equation. Then we have 5y + 40- 40= 100- 40. Which is 5y = 60. At the end, we need to divide 5y by 5, and 100 by 5. And then we get y = 20 which is our solution. [MUSIC]