Question

Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.

Answer 1

Hint: Let us assume that the required number is x. Now we know first we will form an expression for the condition when 5 is subtracted from 5 times the number. Then we will form second expression 4 more than twice the number. Now we will equate both the expression and hence solve the equation to find the value of x.

Complete step-by-step answer:
Now let us say the required number is x. Now we have given conditions, we will form an equation with the help of given conditions.
Now since the required number is x then 5 times the number is 5x. Now when 5 is subtracted from 5 times the number the number becomes 5x – 5.
Now again twice the number is 2x and 4 more than twice the number is nothing but 2x + 4.
Now it is given that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.
Hence we get 5x – 5 = 2x + 4.
Now taking 2x on LHS and 5 on RHS we get 5x – 2x = 5 + 4.
Hence we have 3x = 9.
Now dividing the whole equation by 3 we get x = 3.
Hence the required number is 3.

Note: Now note that whenever we have such word problems always assume the required quantity to be x. Then form expressions according to given condition in general times means multiplication addition means + and subtraction means - . Using this we can form an equation in x. Now we will solve the equation in one variable to find the value of x. Also always remember when shifting terms in the equation the sign of the number or variable changes when taken to the other side of equal to symbol.