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Math Help - Trouble Understanding Word Problems

  1. #1
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    Trouble Understanding Word Problems

    Hi everyone, I am having trouble wrapping my head around a few word problem examples and I have been reading my book over and over and cannot even begin to get anywhere with them.

    Example 1:
    20 peperoni pizzas were delivered at a total cost of $181.
    A sm. pizza costs $5 (contains 3oz. of pepperoni)
    A med. pizza costs $9 (contains 4oz. of pepperoni)
    A lrg pizza costs $12 (contains 5oz. of pepperoni)
    5lbs 2 ounces of pepperoni were used in making these 20 pizzas.
    How many pizzas of each size were delivered?

    Example 2:
    A dietician has two prepackaged mixtures of vitamin additives available for patients. Mixture 1 contains 5 grams of vitamin C and 3 grams of niacin; mixture 2 contains 6 grams of vitamin C and 5 grams of niacin. On an average day she needs 87 grams of niacin and 117 grams of vitamin C. How many packets of each mixture will she need?

    Example 3:
    A twin-engined aircraft can fly 1500 miles from city A to city B in 5 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind and the speed of the plane without any wind?
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  2. #2
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    Quote Originally Posted by lanipr View Post
    Example 1:
    20 peperoni pizzas were delivered at a total cost of $181.
    A sm. pizza costs $5 (contains 3oz. of pepperoni)
    A med. pizza costs $9 (contains 4oz. of pepperoni)
    A lrg pizza costs $12 (contains 5oz. of pepperoni)
    5lbs 2 ounces of pepperoni were used in making these 20 pizzas.
    How many pizzas of each size were delivered?
    let S = number of small pizzas
    M = number of medium pizzas
    L = number of large pizzas

    S + M + L = 20

    S($5) + M($9) + L($12) = $181

    S(3 oz) + M(4 oz) + L(5 oz) = 82 oz

    solve the system of equations for S, M, and L

    Example 2:
    A dietician has two prepackaged mixtures of vitamin additives available for patients. Mixture 1 contains 5 grams of vitamin C and 3 grams of niacin; mixture 2 contains 6 grams of vitamin C and 5 grams of niacin. On an average day she needs 87 grams of niacin and 117 grams of vitamin C. How many packets of each mixture will she need?
    let A = number of packets of mixture 1
    B = number of packets of mixture 2

    A(5 g) + B(6 g) = 117g of vitamin C

    A(3 g) + B(5 g) = 87g of niacin

    solve the system for A and B

    Example 3:
    A twin-engined aircraft can fly 1500 miles from city A to city B in 5 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind and the speed of the plane without any wind?
    let v = no wind speed of airplane
    w = wind speed

    rate x time = distance

    with the wind ...

    (v + w)5 = 1500

    v + w = 300

    against the wind ...

    (v - w)6 = 1500

    v - w = 250

    solve the system for v and w
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  3. #3
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    Thank you!
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