Question

Задание 1Вместо звездочке поставьте такие цифры, чтобы четырехзначное число *74* делилось нацело на 18. Найдите все решенияЗадание 2Галина Васильевна купила три пакета кефира, пачку масла за 45 р., несколько буханок хлеба по 24 р., шесть коробок сничек. Может ли вся ее покупка стоить 260 р., если цена каждого товара выражена целым числом рублей?Даю много баллов за ответы!

Answer 1

Задание 1.
Чтобы число делилось на 18 оно  должно быть четным, т.е. делиться на 2 и сумма цифр должен делиться на 9 (признак делимости на 9). Иначе говоря, 18=2*9, значит число   * 7 4 * , должно делится одновременно на 2 и на 9.
1  -  последняя цифра  0, подбираем первую цифру  0+7+4=11+7=18 :9=2 ==>
                                   7 7 4 0  : 18= 430
2  -  последняя цифра 2, первая цифра  2+7+4=13 + 5 =18 
                                   5 7 4 2   : 18 = 319
3   -  последняя цифра 4 , первая  -    4+7+4=15+3=18
                                   3 7 4 4
Аналогично рассуждая, находим   1746. (последняя цифра увеличивается на 2, первая уменьшается на 2, сумма цифр остается 18).

Задание 2.
Пусть х - цена кефира    3*х - стоимость кефира
                                       45 - стоимость масла
у- кол-во хлеба               24*у - стоимость хлеба
z - цена спичек                 6*z - стоимость спичек
3х+45+24у+6z=260
3(х+15+8у+2z)=260
260 не делится на 3, следовательно сумма покупки не может быть 260.

Answer 2

Task 1: Finding a four-digit number divisible by 18

To find a four-digit number that is divisible by 18, we need to find a number that satisfies two conditions: 1. It is a four-digit number. 2. It is divisible by 18.

Let's break down the problem and find a solution step by step.

1. Four-digit number: A four-digit number has a thousands place, hundreds place, tens place, and units place. The thousands place cannot be zero, as it would make the number a three-digit number. So, let's consider the thousands place as 7.

2. Divisible by 18: A number is divisible by 18 if it is divisible by both 9 and 2. To check if a number is divisible by 9, we can sum its digits and check if the sum is divisible by 9. To check if a number is divisible by 2, we can check if its units place digit is even.

Let's find a number that satisfies these conditions.

1. Thousands place: 7 2. Hundreds place: We can choose any digit from 0 to 9. 3. Tens place: We can choose any digit from 0 to 9. 4. Units place: We can choose any even digit from 0 to 8.

Let's try different combinations to find a number that satisfies both conditions.

- Thousands place: 7 - Hundreds place: 4 - Tens place: 0 - Units place: 8

The number formed is 7408.

Let's check if 7408 is divisible by 18.

- Sum of digits: 7 + 4 + 0 + 8 = 19 - Units place digit: 8 (even)

Since 19 is not divisible by 9, 7408 is not divisible by 18.

Let's try another combination.

- Thousands place: 7 - Hundreds place: 2 - Tens place: 0 - Units place: 0

The number formed is 7200.

Let's check if 7200 is divisible by 18.

- Sum of digits: 7 + 2 + 0 + 0 = 9 - Units place digit: 0 (even)

Since 9 is divisible by 9 and the units place digit is even, 7200 is divisible by 18.

Therefore, the four-digit number that is divisible by 18 is 7200.

Task 2: Calculating the total cost of Galina Vasilyevna's purchase

To determine if the total cost of Galina Vasilyevna's purchase can be 260 rubles, we need to consider the prices of the items she bought.

1. Three packets of kefir: Let's assume the price of each packet of kefir is x rubles. 2. One pack of butter: Let's assume the price of the pack of butter is y rubles. 3. Several loaves of bread: Let's assume the price of each loaf of bread is z rubles. 4. Six boxes of snacks: Let's assume the price of each box of snacks is w rubles.

The total cost of Galina Vasilyevna's purchase can be calculated as follows:

Total cost = (Price of each packet of kefir * 3) + Price of pack of butter + (Price of each loaf of bread * Number of loaves of bread) + (Price of each box of snacks * 6)

We are given that the total cost is 260 rubles. Let's substitute the given prices and solve for x, y, z, and w.

260 = (x * 3) + y + (z * Number of loaves of bread) + (w * 6)

Since the prices of each item are expressed as whole numbers, we can assume that x, y, z, and w are integers.

To find the possible values of x, y, z, and w, we need more information about the number of loaves of bread and the specific prices of each item.

Please provide the number of loaves of bread and the specific prices of each item so that we can calculate the possible values of x, y, z, and w.