Question

За 4 пачки пачки печива та 3 пакети соку заплатили 102 грн. Скільки коштує пачка печива і скільки - пакет соку, якщо пачка печива дешевша від пакета соку на 6 грн?

Answer 1

Х- пакет сока
х-6 - пачка печенья

4*(х-6)+3х=102
4х-24+3х=102
4х+3х=102+24
7х=126
х=126:7
х=18 гривен стоит пакет сока
18-6=12 гривен стоит пачка печенья

проверка
18*3+12*4=102

Answer 2

Calculating the Cost of Cookies and Juice

To solve this problem, we can use a system of equations. Let's denote the cost of a cookie pack as x and the cost of a juice pack as y. We are given the following information:

1. 4 packs of cookies and 3 packs of juice cost 102 UAH. 2. The cost of a pack of cookies is 6 UAH less than the cost of a pack of juice.

We can express this information in the following equations:

1. 4x + 3y = 102 2. x = y - 6

Now, let's solve for the cost of a pack of cookies and the cost of a pack of juice.

Solving the System of Equations

We can use the substitution method to solve the system of equations.

Substitute the value of x from the second equation into the first equation:

4(y - 6) + 3y = 102

Simplify the equation:

4y - 24 + 3y = 102 7y - 24 = 102 7y = 102 + 24 7y = 126 y = 126 / 7 y = 18

Now that we have found the cost of a pack of juice, we can substitute this value back into the second equation to find the cost of a pack of cookies:

x = 18 - 6 x = 12

Conclusion

Therefore, the cost of a pack of cookies is 12 UAH and the cost of a pack of juice is 18 UAH.