Question

Michael uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100\,\text{kg}100kg100, start text, k, g, end text of chocolate in total for his next order. Dark chocolate costs \$12$12dollar sign, 12 per kilogram, milk chocolate costs \$10$10dollar sign, 10 per kilogram, and he wants to spend \$1120$1120dollar sign, 1120 total. Let ddd be the number of kilograms of dark chocolate he buys and mmm be the number of kilograms of milk chocolate he buys.

Answer 1

Answer:

Michael buys 60 kg of dark chocolate and 40 kg of milk chocolate.

Step-by-step explanation:

Let d be the number of kilograms of dark chocolate Michael buys and m be the number of kilograms of milk chocolate he buys.

He needs to buy 100 kg of chocolate in total, then

$d+m=100$

Dark chocolate costs $12 per kilogram, then d kg cost $12d. Milk chocolate costs $10 per kilogram, then m kg cost $10m. Michael wants to spend $1,120 for the chocolate, then

$12d+10m=1,120$

From the first equation

$d=100-m$

Substitute it into the second equation:

$12(100-m)+10m=1,120\\ \\1,200-12m+10m=1,120\\ \\-12m+10m=1,120-1,200\\ \\-2m=-80\\ \\m=40\\ \\d=100-m=100-40=60$

Michael buys 60 kg of dark chocolate and 40 kg of milk chocolate.