Smart search for an unknown number
(1) If you subtract a number from three times that number, the result is 25. 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 550 €. How much € do I have in each pocket?
(3) The sum of a natural number and the next number is 257. Set up an equation and solve the problem.
(4) The sum of a number and its half is equal to 68. What is that number?
(5) Mia asks John 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 John if he is older than 17 years?
(6) Double a number decreased by 13 is equal to 27. What is that number?
(7) A number plus double the previous number is equal to 32. What are those numbers?
(8) The sum of the fifth and sixth parts of a number is 50 mg less than its half. What is the recommended daily amount of cholesterol in mg?
(9) The perimeter of a triangle is 33 cm, and the sides are three consecutive numbers. What is the length of each side?
(10) James says to Evelyn: I have twice as many euros as you. If together they have 30 euros, how much does each have?
(11) The sum of three consecutive numbers is 48. What are those numbers?
(12) What number, increased by its half and its third, gives the sum 125?
(13) Isla is 6 years older than three times the age of Xavi. If together they are 86 years old, how old is each?
(14) The sum of double a number and an additional 19 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 54 cm. What is the length of each side?
(16) Oliver bought 5 notebooks, and each costs 9 kuna. If she paid a total of 180 kuna, how much change did she receive?
(17) What number multiplied by 2 and increased by 12 gives the result 85?
(18) Arthur saved three times as much as Robert. If together they saved 100 €, 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.
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