Creating Linear Equations in One Variable

[RepeaterCreeper]

Question #1: 'The area of Sofia's herb garden is 1/8 the area of her vegetable garden. The area of her herb garden is 6 square feet. What is the area of her vegetable garden.'

Question #2: 'It cost Justin $100 to have a cable TV installed in his house. Each month he pays an access fee plus tax of 7% of his monthly bill. After 6 months, Justin had paid a total of $350.38 for his access fee, taxes, and his initial installation. What is Justin's monthly access fee not including taxes.'

So I suck at fractions and do not understand how these problem gets solved. If someone could explain to me how these problems gets solved I would really appreciate it.

 

[ksdhart]

Question #1 is fairly straightforward - it just needs to be translated from English to Math. You're given the area of Sofia's herb garden, and you're told that it is one eighth of the total area of the whole vegetable garden. Remember that in these types of problems "of" is a keyword telling you to multiply. If we call the vegetable garden's area v, then 1/8 of v is 6 square feet. Now what would your equation look like? And can you solve that equation?

Question #2 is more complicated to set up, but I think once you get the equation set up, you'll be able to handle it. In math problems, one of my first steps is to identify any unknown values and give them variables. In this case, you're given the initial set-up fee, but you don't know the monthly bill. You don't know the precise value of the tax either, but you are told that it is 7% of the monthly bill. So, we'll call the single unknown, the monthly bill, b. Every month Justin pays the monthly bill plus his tax. So, can you write an expression for how much he pays each month? Once you have that, you know that he paid for 6 months of cable. So, modify the expression that it reflects six months of payments instead of just one month. Then add in the initial set-up fee, and that final expression you have will be equal to the given value of $350.38.

Hopefully, these are hints enough to get you started on your way. If you get stuck, please show all your work you've done (even if you know it's wrong) when you reply back. Good luck.