Taj has three scoops for measuring flour. The largest scoop holds 2 1/2 times as much as the smallest one. The middle scoop holds 1 3/4 times as much as the smallest one. What are two different ways in which Taj could measure each of the following?

a) 3 1/4 times as much as the smallest
scoop holds
b) 1/2 as much as the smallest scoop holds

Answer 1

a) #3.25C = 2.5C + 1.75C - C#
Put ONE of A and B into the bowl, and take OUT ONE of C.

b) #0.5C = 2.5C - 2C# "B" is not needed. Put ONE of A into the bowl, and take OUT TWO of C.

First, you can set up all of the measures as related to the smallest one: #A = 2.5C#; #B = 1.75C# Or, #C = A/2.5#; #C = B/1.75#. With these we can make the combinations easier. Each combination must be some addition of the available cups: Desired Volume #= xA + yB + zC# With our derived ratios, this becomes: Desired Volume #= x(2.5C) + y(1.75C) + zC#
a) #3.25C = 2.5C + 1.75C - C# Put ONE of A and B into the bowl, and take OUT ONE of C.
b) #0.5C = 2.5C - 2C# "B" is not needed. Put ONE of A into the bowl, and take OUT TWO of C.
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Answer 2

Sure, here are two different ways Taj could measure each of the following using the scoops:

  1. Largest Scoop: 2 1/2 cups Middle Scoop: 1 3/4 cups Smallest Scoop: 1 cup

    • 5 cups: Using the largest scoop twice.
    • 6 3/4 cups: Using the middle scoop thrice.
  2. Largest Scoop: 5 cups Middle Scoop: 3 1/2 cups Smallest Scoop: 2 cups

    • 10 cups: Using the largest scoop twice.
    • 7 cups: Using the middle scoop twice and the smallest scoop once.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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