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}100

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.

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Lyla 1 week 2021-11-25T16:12:36+00:00 1 Answer 0 views 0

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    2021-11-25T16:14:11+00:00

    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.

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