# Thread: Solving equations, a couple questions!

1. ## Solving equations, a couple questions!

I have these questions on my homework but I have no idea how the answer is how it is. Thank you for answering!

1. Solve this equation for C.
S=C+rC
I know that the answer is S/1+r= c
I do not know where the 1 comes from.

2. You have 36.75$to spend on a sweathshirt. There is a 5% sales tax. What is the most the sweatshirt can cost? How do you solve this? 3. Solve this equation for B1: A=1/2h (b1 + b2) The answer is 2a/h -b1 Whenever I do it, I get 2a-b1/h I do not know what I am doing wrong. 4. A garden is 46 feet wide and 84 feet long. The garden has a path around it that is 10 feet wide. The cost of fencing is 9$ per foot. How much will it cost to put a fence around the path?

Here, I do not get how to draw a picture or get the equation.

Thank you so much to anyone who takes the time to answer all of my questions! I have a midyear on monday and I really need to know these answers for it.

2. Originally Posted by cherrybaby
I have these questions on my homework but I have no idea how the answer is how it is. Thank you for answering!

1. Solve this equation for C.
S=C+rC
I know that the answer is S/1+r= c
I do not know where the 1 comes from.
S = C +rC

S = C(1 + r)

(We factored out the C)

Divide by (1 + r)

Thus, S/(1 + r) = C

3. Originally Posted by cherrybaby

2. You have 36.75$to spend on a sweathshirt. There is a 5% sales tax. What is the most the sweatshirt can cost? How do you solve this? 3. Solve this equation for B1: A=1/2h (b1 + b2) 2. You want the sweatshirt to cost, at most, x + .05x <=$36.75

Solve for x;

1.05x = 36.75

x = 35

Thus, you want the sweatshirt to cost, AT MOST, $35. Check:$35*(.05) = $1.75 (this is the sales tax)$35 + $1.75 =$36.75;

If the sweatshirt is any more, the sales tax would be greater and thus would exceed this amount.

3. A = (1/2)*h*(b_1 + b_2)

Multiply by 2;

2A = h*(b_1 + b_2)

Divide by h;

2A/h = b_1 + b_2

2A/h - b_1 = b_2

4. Originally Posted by cherrybaby
4. A garden is 46 feet wide and 84 feet long. The garden has a path around it that is 10 feet wide. The cost of fencing is 9$per foot. How much will it cost to put a fence around the path? Here, I do not get how to draw a picture or get the equation. Soroban, I am sure, will be able to draw you a nice picture. I am not sure how to, unfortunately. Any way; The garden alone is 84 x 46; But, since we have a path around it that is 10 feet wide, we have to include 5 feet on each side; Thus, it's 89 feet long by 51 feet wide; The question is asking for the perimeter; 2W + 2L = P 2(51) + 2(89) = 280 feet of fencing But, we have that it is$9 per foot; thus,

280*9 = $2520 5. Thank You so much for responding aftershock! My only problem is with the last problem, where I know that the answer is 3060, and I do not know how to get that answer. (I was supplied with an answer key, but it does me know me good.) 6. Originally Posted by cherrybaby Thank You so much for responding aftershock! My only problem is with the last problem, where I know that the answer is 3060, and I do not know how to get that answer. (I was supplied with an answer key, but it does me know me good.) Stupid question if you ask me; two ways of interpreting it. They are interpreting it as follows: The garden alone is 84 x 46; Now, the path is 10 feet wide all around; thus, 10 at the top and 10 at the bottom, and 10 on each of the sides... So 104, 104, 66, 66; P = 2(104) + 2(66) = 340 340*9 =$3060