Question

Даша купила 3 набора открыток. В первом наборе в 5 раз больше открыток, чем во втором, а в третьем на 8 открыток меньше, чем в первом. Если к первому набору добавить ещё 24 открытки, то количество открыток в нём будет равно количеству открыток во втором и третьем наборах вместе. Сколько открыток было в каждом из купленных наборов?

Answer 1

х-открыток во втором наборе

5х-открыток в первом наборе

5х-8-открыток в третьем наборе

5х+24=х+5х-8

6х-х=24+8

х=32 открытки во втором наборе

32*5=160 открыток в первом наборе

160-8=152 открыток в третьем наборе

 

160+24=32+152

     184=184

Answer 2

х - второй

5х - первый

5х-8 - третий

 

5х+24=х+5х-8

х=32 - второй

5*32=160 - первый

160-8=152 - третий

Answer 3

Solution:

Let's solve the problem step by step.

Step 1: Define the Variables - Let's assume the number of postcards in the second set is represented by x. - The number of postcards in the first set is 5 times more than the second set, so it is 5x. - The number of postcards in the third set is 8 less than the first set, so it is 5x - 8.

Step 2: Formulate the Equation - According to the problem, if 24 postcards are added to the first set, it will be equal to the total number of postcards in the second and third sets combined. - This can be represented as: 5x + 24 = x + (5x - 8).

Step 3: Solve the Equation - Let's solve the equation to find the value of x.

Step 4: Calculate the Number of Postcards in Each Set - Once we find the value of x, we can calculate the number of postcards in each set.

Calculation:

Step 1: Define the Variables - Let x = the number of postcards in the second set. - The number of postcards in the first set = 5x. - The number of postcards in the third set = 5x - 8.

Step 2: Formulate the Equation - 5x + 24 = x + (5x - 8)

Step 3: Solve the Equation - Simplifying the equation: 5x + 24 = x + 5x - 8 - Combining like terms: 5x + 24 = 6x - 8 - Rearranging terms: 24 + 8 = 6x - 5x - Solving for x: 32 = x

Step 4: Calculate the Number of Postcards in Each Set - The number of postcards in the second set (x) = 32. - The number of postcards in the first set = 5x = 5 * 32 = 160. - The number of postcards in the third set = 5x - 8 = 5 * 32 - 8 = 152.

Answer:

- Dasha bought 160 postcards in the first set, 32 postcards in the second set, and 152 postcards in the third set.