Question

The quotient of a number and -7 decreased by 2 is 10. How do you find the number?

Answer 1

Hint:In order to express a mathematical problem explained in words we have to take all the relevant and important information mentioned in the word problem and represent it in a much easier way like an equation. The given information has to be expressed algebraically. Algebraic expressions are expressions which are made up of variables and constants along with mathematical algebraic operations which are addition, subtraction, multiplication, division etc.

Complete step by step answer:
Given statement: ${\text{Quotient of a number and}} - 7{\text{ decreased by }}2{\text{ is }}10...................\left( i \right)$
Now let the unknown number be $x$.Now let’s split the statement (i) into two parts.
1. Quotient of a number and$ - 7$.
2. Decreased by the number $2$we get$10$.

Now take each part separately:
1. We know that quotient is the term given to the expression which is obtained by dividing one term or number over another term or number or simply quotient is the result of the process of division.Such that we write that the statement: quotient of a number and $ - 7$ mathematically as:
$\dfrac{x}{{ - 7}}.............................\left( {ii} \right)$
Now we take the result in (ii) and simply apply the 2nd condition:
2. Such that mathematically we can write the statement decreased by the number $2$ we get $10$ as:
$\dfrac{x}{{ - 7}} - 2 = 10.....................................\left( {iii} \right)$
Now on simplifying the equation (ii) we can find $x$ and which is the unknown number.
Such that:
$\Rightarrow \dfrac{x}{{ - 7}} - 2 = 10 \\
\Rightarrow \dfrac{x}{{ - 7}} = 10 + 2 \\ $
$\Rightarrow \dfrac{x}{{ - 7}} = 12 \\
\Rightarrow x = 12 \times - 7 \\
\therefore x = - 84...........................\left( {iv} \right) \\ $
There the unknown number which satisfies the statement ‘The quotient of a number and -7 decreased by 2 is 10’ is $ - 84$.

Note:While writing an algebraic expression some of the commonly used words and their corresponding mathematical operations are given below:
1. Addition : plus, sum, more than
2. Subtraction : subtracted, minus, less than, decreased by
3. Multiplication : times, product
4. Division : divided, quotient
Also while making an algebraic expression one must take care that the words and the operations used are mathematically correct or not.