Tablespoons Cups
4 64
5 80
6 96
7 112

A. The number of table spoons is 1/16 of the number of cups.

B. The number of tablespoons is 1/4 of the number of cups.

C. The number of tablespoons is 4 times the number of cups.

D. The number of tablespoons is 16 times the number of cups.
 

in Word Problem Answers by Level 10 User (57.4k points)

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1 Answer

this is a simple question about reducing ratios - but also reducing problems.  My first step here would be to get rid of the fluff.

We don't care here about what a tablespoon or cup actually is, we just care about the table.  So my first step would be to translate this problem into something like this:

Based on the table below, what is the relationship between X and Y?

X   Y

4   64

5   80

6   96

7   112

There's a reason it may be important to do this; if you are familiar with tablespoons and cups already, you know that there are many more tablespoons in a cup than the other way round.  This can confuse you and ultimately has you focusing on not the math, which is the wrong thing to do.

Now that we have a more straightforward thing to work with, take the first set of X/Y values...

4   /   64 

...and divide both by the smaller number...

4/4 = 1

64/4 = 16

...so we get....

4 / 64 = 1 / 16

...so far, so good.  we need to be sure though, so let's check that against the other numbers in the table, by multiplying our X by 16 so we can see if it matches our Y.  Here's the formula...

16x = 1y

...so...

16 (5) = 80

..that checks out.  Try the rest on your own.

by

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