The number of paper clips that crystal has is 42 divided by the number of paper clips that gayle has. if gayle has 11 more paper clips than crystal does, how many paper clips does each have

• Gayle: 14

• Crystal: 3

Step-by-step explanation:

Let g represent the number of paperclips Gayle has. Then 42/g is the number Crystal has. The relationship between the two numbers is said to be ...

g - (42/g) = 11

Multiplying by g gives ...

g^2 -42 = 11g

g^2 -11g -42 = 0 . . . . subtract 11 g to put into standard form

To factor this, you are looking for two factors of -42 that sum to -11.

-42 = -42·1 = -21·2 = -14·3 = -7·6

You can see that -14 and 3 sum to -11, so the factoring is ...

(g -14)(g +3) = 0

g = 14 . . . . . . . . . . makes the product zero. (The g=-3 solution is extraneous.)

Gayle has 14 paperclips and Crystal has 3.

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