Smart search for an unknown number


(1) If you subtract a number from three times that number, the result is 35. What is that number?

(2) In one pocket, I have a certain amount of money, and in the other, I have double that amount. In total, I have 150 €. How much € do I have in each pocket?

(3) The sum of a natural number and the next number is 239. Set up an equation and solve the problem.

(4) The sum of a number and its half is equal to 54. What is that number?

(5) Sophia asks Robert how old he is, and he replies: half of my age, plus a third, plus a quarter, plus a sixth of my age add up. How old is Robert if he is older than 20 years?

(6) Double a number decreased by 12 is equal to 32. What is that number?

(7) A number plus double the previous number is equal to 17. What are those numbers?

(8) The sum of the fifth and sixth parts of a number is 25 mg less than its half. What is the recommended daily amount of cholesterol in mg?

(9) The perimeter of a triangle is 15 cm, and the sides are three consecutive numbers. What is the length of each side?

(10) Henry says to Ava: I have twice as many euros as you. If together they have 24 euros, how much does each have?

(11) The sum of three consecutive numbers is 75. What are those numbers?

(12) What number, increased by its half and its third, gives the sum 145?

(13) Oscar is 12 years older than three times the age of Steve. If together they are 72 years old, how old is each?

(14) The sum of double a number and an additional 13 is equal to triple that number. What is that number?

(15) A triangle has two equal sides and one side that is 5 cm shorter. The total perimeter of the triangle is 46 cm. What is the length of each side?

(16) Elijah bought 5 notebooks, and each costs 10 kuna. If she paid a total of 145 kuna, how much change did she receive?

(17) What number multiplied by 5 and increased by 12 gives the result 100?

(18) John saved three times as much as James. If together they saved 95 €, how much did each save?

Instructions:

Solving a Single-Variable Equation

This is an example of solving a simple linear equation step by step.

Problem:

\( 3x + 5 = 14 \)

Solution:

Step 1: Subtract 5 from both sides.

\( 3x + 5 - 5 = 14 - 5 \)

\( 3x = 9 \)

Step 2: Divide both sides by 3.

\( \frac{3x}{3} = \frac{9}{3} \)

Solution: \( x = 3 \)

Check: Substitute \(x = 3\) back into the original equation.

\( 3(3) + 5 = 9 + 5 = 14 \)

Since \( 14 = 14 \), the solution is correct.