A gardener wants to create a rectangular vegetable garden in a backyard. She wants to have a total area of 13 square feet, and it should be 12 feet longer than it is wide. What dimensions should she use for the vegetable garden?

a. 1 feet by 13 feet
b. 3 feet by 15 feet
c. 6 feet by 9 feet
d. 5 feet by 17 feet

a. 1 feet by 13 feet

Step-by-step explanation:

Let L represent the length of the rectangular vegetable garden.

Let W represent the width of the rectangular vegetable garden.

She wants to have a total area of 13 square feet. This means that

LW = 13 - - - - - - - - - - -1

The garden should be 12 feet longer than it is wide. This means that

L = W + 12

Substituting L = W + 12 into equation 1, it becomes

W(W + 12) = 13

W² + 12W = 13

W² + 12W - 13 = 0

W² + 13W - W - 13 = 0

W(W + 13) - 1(W + 13)

W - 1 = 0 or W + 13 = 0

W = 1 or W = - 13

Since the width cannot be negative, then W = 1 feet

L = W + 12 = 1 + 12

L = 13 feet

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

answer: 1, 3 and 5 are correct

step-by-step explanation: