Question

Сахар составляет три пятых части варенья, а остальную часть вишня. Вишни на 2 кг. меньше, чем сахара. Какова масса варенья?

Answer 1

Все варенье соствляет 1. найдем, сколько частей занимает вишня: 1 - 3/5 = 5/5 - 3/5 =2/5 (частей отвсего варенья) Расчитаем насколько частей сахара больше в вишни: 3/5 - 2/5 =1/5 Так же сказано в условии, что вишни в варенье на 2 кг меньше, чем сахар, т.е как раз 1/5 части это и есть 2 кг. Но у нас сахара 3/5, т.е 3/5 = 3*(1/5)=3*2=6 (кг) -сахара. А вишни у нас 2/5, т.е 2/5=2*(1/5)=2*2=4 (кг) - вишни Посчитаем общую массу варенья: 6+4 = 10 (кг) Ответ: 10 кг варенья.

Answer 2

Calculating the Mass of Jam

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

Given: - Sugar makes up three-fifths of the jam, and the rest is cherries. - There are 2 kg less cherries than sugar.

Let's denote the mass of sugar as S and the mass of cherries as C.

From the given information, we can set up the following equations: 1. S = (3/5)(S + C) (Sugar makes up three-fifths of the jam) 2. C = S - 2 (There are 2 kg less cherries than sugar)

We can solve these equations to find the masses of sugar and cherries, and then calculate the total mass of jam.

Solving for the Masses of Sugar and Cherries

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: 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 = C + 2 S = 4 + 2 S = 6 kg

Calculating the Total Mass of Jam

The total mass of jam is the sum of the masses 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.