Question

The total mass of 7 big sacks of sugar and 2 small sacks of sugar is 94 kg. The total mass of 3 big sacks of sugar and 3 small sacks of sugar is 51 kg. Find the mass of 1 big sack of sugar.

Answer 1

7b + 2s = 94

3b + 3s = 51

Multiply first equation by 3.

21b + 6s = 282

Multiply second equation by 2.

6b + 6s = 102

Subtract second equation from first. I'll let you take it from here.

Answer 2

3 big sacks + 3 small sacks→51kg

1 big sack + 1 small sack = 51 kg ÷ 3 = 17 kg
2 big sacks + 2 small sacks → 2 × 17 kg = 34 kg 5 big sacks → 94 kg – 34 kg = 60 kg
1 big sack → 60 ÷ 5 = 12
The mass of 1 big sack of sugar is 12 kg.

Answer 3

[AI-generated answer — Explain Bot]

To find the mass of 1 big sack of sugar, let's set up a system of equations based on the given information.

Let's assume the mass of one big sack of sugar is 'B' kg, and the mass of one small sack of sugar is 'S' kg.

From the first equation, we can write:
7B + 2S = 94 (Equation 1)

From the second equation, we can write:
3B + 3S = 51 (Equation 2)

Now, we need to solve these equations simultaneously to find the values of B and S.

To eliminate the 'S' variable, we can multiply Equation 2 by 2:
6B + 6S = 102

Now, subtract Equation 1 from this new equation:
6B + 6S - (7B + 2S) = 102 - 94
6B + 6S - 7B - 2S = 8
-B + 4S = 8 (Equation 3)

Now we have two equations to work with:
7B + 2S = 94 (Equation 1)
-B + 4S = 8 (Equation 3)

To solve this system of equations, we can use any method like substitution or elimination.

Let's use the elimination method:
Multiply Equation 3 by 7:
-7B + 28S = 56

Now, add Equation 1 to this new equation:
7B + 2S + (-7B + 28S) = 94 + 56
2S + 28S = 150
30S = 150
Divide both sides by 30:
S = 5

Now, substitute the value of S = 5 into either Equation 1 or Equation 3. Let's use Equation 1:
7B + 2(5) = 94
7B + 10 = 94
Subtract 10 from both sides:
7B = 84
Divide both sides by 7:
B = 12

Therefore, the mass of one big sack of sugar is 12 kg.