Question

How do you translate the phrase “six more than twice a number is 16” to an equation? What is the value of the number?

Answer 1

Hint: Now we are given a sentence and we want to convert it into a mathematical equation. Now note that twice is nothing but two times. Now first we will break the equation and write its mathematical translation by replacing more by addition and times by multiplication. Hence we will write the whole equation in mathematical form.

Complete step by step solution:
Now we want to translate the given sentence into a mathematical equation.
First let us consider the given sentence “six more than twice a number is 16”
Now let us see the translation of each word.
Six more in mathematics means addition of 6. Hence six more is written as + 6.
Now let the number be x. Then twice a number means two times a number. hence mathematically we write it as 2x.
Now we can write six more twice a number as 2x + 6.
Now we are given that six more than twice a number is 16 hence we can say that the value of equation 2x + 6 is 16.
Hence we get, 2x + 6 = 16.
Now let us find the value of x for which the equation is true.
Now consider the equation 2x + 6 = 16.
Subtracting 6 on both sides of the equation we get, 2x + 6 – 6 = 16 – 6.
Hence we have 2x = 10.
Now dividing the whole equation by 2 we get, x = 5.
Hence the solution of the equation is 5.

Note:
Now note that while converting a word problem into mathematical equation always break the sentences into parts. Now converting the words into mathematical equations such as more is replaced by addition times is replaced by multiplication. Always use a variable to represent a number. Hence we can easily write an equation for any expression.