Problem of the Week - Algebra and Up - Feb. 7, 2021 to Feb. 13, 2021

Algebra and Up: 

Question: A chocolatier receives an order for a 10-pound chocolate statue whose cacao content is exactly 40%. The chocolatier has 20% cacao chocolate and 50% cacao chocolate at his disposal. How many pounds of each does he need to melt together to have exactly the right amount for the statue? 

Answer: 

3 1/3 pounds of 20% cacao chocolate and 6 2/3 pounds of 50% cacao chocolate

Solution: 

40% of 10 pounds of chocolate is 4 pounds, so we know that the total amount of cacao in the mixture must be 4 pounds. We can set up an equation to solve for x, the amount of 20% cacao chocolate:

0.20x + 0.50(10 – x) = 4

Notice that the amount of 50% cacao chocolate is 10 – x. This is because every part of the 10 pounds of chocolate that isn’t the 20% cacao is the 50% cacao. When we solve for x, we find that x = 3 1/3. That means that there are 3 1/3 pounds of 20% cacao, so there must be 10 – 3 1/3 = 6 2/3 pounds of 50% cacao.