Ivan Shishkin, Rye (1878)

Problems/General algebraUnreviewed

A delicious example of cross-multiplication

by Catalpa·
4
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 110First steps / middle schoolPremiers pas / collège
  2. 1125Beginner / high schoolDébutant / lycée
  3. 2650Intermediate / undergraduateIntermédiaire / licence
  4. 5170Advanced / graduateAvancé / master
  5. 7190Expert / specializedExpert / spécialisé
  6. 91100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Lacking inspiration for a dessert for a gala dinner, you come across the following recipe:

V.'s Recipe for a Super Moist Chocolate Cake

Ingredients
Serves 6

  • 200g dark chocolate
  • 130g butter
  • 6 eggs
  • 1 tablespoon flour
  • 150g powdered sugar

Melt the chocolate and butter together.
Mix the eggs, flour, and powdered sugar until the mixture is slightly frothy. Then add the melted chocolate and butter, which have been allowed to cool slightly to prevent the eggs from cooking.
Pour the mixture into a baking pan and bake at 150–160°C for at least 20 minutes (depending on the oven’s heat, baking may take up to 40 minutes).

  1. The diner will be served for 8 people: thanks to cross-multiplications, compute the new quantities of the ingredients.
  2. A few weeks later, it’s your mother’s birthday, but you only have 5 eggs left, and the supermarket next door is out of stock! How many people can you invite (besides you and your mother) so that everyone can have some cake?
  3. You’re already in the middle of baking the birthday cake when you realize you only have 130g of powdered sugar left... Will you have enough of it to make the cake mentionned in the previous question?
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