Smart search for an unknown number
(1) If you subtract a number from three times that number, the result is 36. 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 500 €. How much € do I have in each pocket?
(3) The sum of a natural number and the next number is 145. Set up an equation and solve the problem.
(4) The sum of a number and its half is equal to 32. What is that number?
(5) Liam asks Arthur 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 Arthur if he is older than 19 years?
(6) Double a number decreased by 7 is equal to 20. What is that number?
(7) A number plus double the previous number is equal to 16. What are those numbers?
(8) The sum of the fifth and sixth parts of a number is 55 mg less than its half. What is the recommended daily amount of cholesterol in mg?
(9) The perimeter of a triangle is 36 cm, and the sides are three consecutive numbers. What is the length of each side?
(10) Popay says to Evelyn: I have twice as many euros as you. If together they have 32 euros, how much does each have?
(11) The sum of three consecutive numbers is 60. What are those numbers?
(12) What number, increased by its half and its third, gives the sum 60?
(13) Lily is 14 years older than three times the age of Xavi. If together they are 56 years old, how old is each?
(14) The sum of double a number and an additional 18 is equal to triple that number. What is that number?
(15) A triangle has two equal sides and one side that is 2 cm shorter. The total perimeter of the triangle is 56 cm. What is the length of each side?
(16) Harper bought 5 notebooks, and each costs 13 kuna. If she paid a total of 175 kuna, how much change did she receive?
(17) What number multiplied by 5 and increased by 22 gives the result 75?
(18) Robert saved three times as much as James. If together they saved 80 €, 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.