Jarod and the Bunnies.

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Presentation transcript:

Jarod and the Bunnies

We’re asked to find the length and width of the garden, so … Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 3 times the width. He needs 50 feet of fencing to do the job. Find the length and width of the garden. We’re asked to find the length and width of the garden, so … Let W = the width of the garden Let L = the length of the garden

Our first equation is L = 3W + 9 Now we need to find out two relationships between the length and the width: 1) The length of the garden is 9 feet more than 3 times the width. The length of the garden L is = 9 feet more than 3 times the width 3W + 9 NOTE: than reverses the order. The 9 came first in English and comes last in algebra. Our first equation is L = 3W + 9

We need one more relationship between the length and the width: 2) He needs 50 feet of fencing to do the job. All the way around the garden would be: L W W All the way around is W + L + W + L or 2L + 2W = 50

Now we have two equations in two unknowns L = 3W + 9 2L + 2W = 50 I would solve this by substitution 2(3W + 9) + 2W = 50 6W + 18 + 2W = 50 8W + 18 = 50 8W = 32 W = 4

Now let’s find the length of the garden and check our work L = 3W + 9 W = 4 L = 3(4) + 9 L = 12 + 9 L = 21 Now we have that the width is 4 and the length is 21. Does this fit our story? The length of the garden is 9 feet more than 3 times the width. L = 3(4) + 9 = 12 + 9 = 21 so far so good! 2W + 2L = 50 2(4) + 2(21) = 50 8 + 42 = 50 We have a winner! Length = 21 and width = 4