Question

Сахар составляет 3/5 вишневого варенья а остальную часть - вишня. Вишни в варенье на 2 кг меньше чем сахара. Какова масса варенья?

Answer 1

Х - масса всего варенья. Пусть $\frac{3}{5} x=0,6х$ - масса сахара, $\frac{2}{5} x=0,4х$ - масса вишни. По условию задачи разница между вишней и сахаром - это 2 кг.

0,6х-0,4х=2
0,2х=2
х=2:0,2
х=10 кг - варенья

Ответ: 10 кг - масса варенья.

Answer 2

Calculating the Mass of Jam

To calculate the mass of the jam, we can use the given information about the proportions of sugar and cherries in the jam.

Given: - Sugar makes up 3/5 of the cherry jam. - The rest of the jam is cherries. - The amount of cherries in the jam is 2 kg less than the amount of sugar.

Let's denote: - S: Mass of sugar - C: Mass of cherries

We can set up the following equations based on the given information: 1. S = (3/5)(S + C) (Sugar makes up 3/5 of the jam) 2. C = S - 2 (The amount of cherries is 2 kg less than the amount of sugar)

Solving the Equations

We can solve these equations to find the mass of the jam.

First, let's solve equation 2 for S: S = C + 2

Now, substitute this value of S into equation 1: (C + 2) = (3/5)(C + 2 + C)

Simplify the equation: (C + 2) = (3/5)(2C + 2)

Expand and solve for C: 5(C + 2) = 3(2C + 2) 5C + 10 = 6C + 6 10 - 6 = 6C - 5C 4 = C

So, the mass of cherries (C) is 4 kg.

Now, we can find the mass of sugar (S): S = C + 2 S = 4 + 2 S = 6 kg

Calculating the Total Mass of Jam

Finally, we can calculate the total mass of the jam by adding the mass of sugar and cherries: Total mass = S + C Total mass = 6 kg + 4 kg Total mass = 10 kg

Therefore, the mass of the jam is 10 kg.