Question

Костя и Серёжа решили взвесить любимые игрушки. Динозавра машинку и пирамидку. Если убрать пирамидку, весы показывают, 500 гр. Если машинку, то динозавр и пирамида-250 грамм. Если без динозавра, машина и пирамида - 350 грамм. Сколько весят 3 игпущки

Answer 1

УСЛОВИЕ
D+M=500
D+P=250
M+P=350
РЕШЕНИЕ
2D+2M+2P=500+250+350=1100
D+M+P=1100/2=550
P=550-500=50
M=550-250=300
D=500-300=200

Answer 2

Problem Analysis

Kostya and Sergey are weighing their favorite toys: a dinosaur, a car, and a pyramid. The weights of the toys are given under different conditions. We need to determine the weight of three toys together.

Solution

Let's analyze the given conditions and calculate the weight of each toy.

1. If the pyramid is removed, the scales show 500 grams. 2. If the car is removed, the weight of the dinosaur and the pyramid is 250 grams. 3. If the dinosaur is removed, the weight of the car and the pyramid is 350 grams.

Let's assign variables to the weights of the toys: - Weight of the dinosaur: D - Weight of the car: C - Weight of the pyramid: P

Based on the given conditions, we can set up the following equations:

1. If the pyramid is removed, the scales show 500 grams: - Equation 1: D + C = 500 2. If the car is removed, the weight of the dinosaur and the pyramid is 250 grams: - Equation 2: D + P = 250 3. If the dinosaur is removed, the weight of the car and the pyramid is 350 grams: - Equation 3: C + P = 350 We now have a system of three equations with three variables. We can solve this system to find the weights of the toys.

Solving the System of Equations

To solve the system of equations, we can use various methods such as substitution or elimination. Let's use the elimination method to find the values of D, C, and P.

Adding Equation 2 and Equation 3, we get: - D + P + C + P = 250 + 350 - D + C + 2P = 600

Substituting Equation 1 into the above equation, we have: - 500 + 2P = 600 - 2P = 600 - 500 - 2P = 100 - P = 50

Now, substituting the value of P into Equation 2, we get: - D + 50 = 250 - D = 250 - 50 - D = 200

Similarly, substituting the value of P into Equation 3, we get: - C + 50 = 350 - C = 350 - 50 - C = 300

Therefore, the weights of the toys are: - Weight of the dinosaur (D) = 200 grams - Weight of the car (C) = 300 grams - Weight of the pyramid (P) = 50 grams

Calculating the Weight of 3 Toys Together

To calculate the weight of the three toys together, we simply add their individual weights: - Weight of 3 toys = Weight of the dinosaur + Weight of the car + Weight of the pyramid - Weight of 3 toys = 200 grams + 300 grams + 50 grams - Weight of 3 toys = 550 grams

Therefore, the weight of the three toys together is 550 grams.

Conclusion

Kostya and Sergey's favorite toys weigh 550 grams when weighed together. The weight of the dinosaur is 200 grams, the weight of the car is 300 grams, and the weight of the pyramid is 50 grams.

Please let me know if there's anything else I can help you with!