Une bouteille et son bouchon pèsent 110 g . La bouteille pèse 100 g de plus que le bouchon. Quel est le poids de la bouteille ? quel est le poids du bouchon?

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Let's denote the weight of the bottle as $$ B $$ grams and the weight of the cap as $$ C $$ grams.

From the given information:
1. The bottle and its cap weigh a total of 110 grams: $$ B + C = 110 $$ grams.
2. The bottle weighs 100 grams more than the cap: $$ B = C + 100 $$.

We can solve these two equations to find the weights of the bottle and the cap.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}B+C=110\B=C+100\end{array}ight.$$
- step1: Substitute the value of $$B:$$
  $$C+100+C=110$$
- step2: Add the terms:
  $$2C+100=110$$
- step3: Move the constant to the right side:
  $$2C=110-100$$
- step4: Subtract the numbers:
  $$2C=10$$
- step5: Divide both sides:
  $$\frac{2C}{2}=\frac{10}{2}$$
- step6: Divide the numbers:
  $$C=5$$
- step7: Substitute the value of $$C:$$
  $$B=5+100$$
- step8: Simplify:
  $$B=105$$
- step9: Calculate:
  $$\left\{ \begin{array}{l}B=105\C=5\end{array}ight.$$
- step10: Check the solution:
  $$\left\{ \begin{array}{l}B=105\C=5\end{array}ight.$$
- step11: Rewrite:
  $$\left(B,Cight) = \left(105,5ight)$$
The solution to the system of equations is $$ B = 105 $$ grams and $$ C = 5 $$ grams.

Therefore, the weight of the bottle is 105 grams and the weight of the cap is 5 grams.
La bouteille pèse 105 grammes et le bouchon pèse 5 grammes.

Une bouteille et son bouchon pèsent 110 g . La bouteille pèse 100 g de plus que le bouchon. Quel est le poids de la bouteille ? quel est le poids du bouchon?

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