Write an equation and solve?

Question

You are taking horseback lessons. The introductory lesson is 2/3 the cost of each additional lesson. If you take 6 lessons and spend a total of $340. How much was the introductory lesson?

You purchase 3 bags of fertilizer for your garden. Each bag contains 50 cubic feet of fertilizer. If the fertilizer is spread a single foot thick and the length of the garden is 5 more than a width, what are the garden's dimensions?

Please if you can help with any of these I would appreciate it. I am so horrible in math.

Thank you :]

Answer 1

Let x be the cost of each additional lesson.  Then the introductory lesson is 2/3 x

2/3 x + 5x = 340

To solve, multiply each term by 3 to get rid of the fraction

2x+15x=1020

17x=1020

x=1020/17=$60

The introductory lesson was (2/3)* 60=$40

You have 50*3=150 cubic feet of fertilizer

Let the width of the garden be x.  Then the length of the garden is x+5.  You are given that the height is 1.  The length times the width times the height is the volume, which you know is 150 cubic feet.

x*(x+5)*1=150

x²+5x=150

x²+5x-150=0

(x+20)(x-15)=0

x=-20 or x=15.  Throw out the negative answer because you can't have negative width.

The width is 15 feet and the length is 15*5=75 feet

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