# Solving equations, a couple questions!

• Jan 20th 2007, 10:25 AM
cherrybaby
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)

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.
• Jan 20th 2007, 10:33 AM
AfterShock
Quote:

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
• Jan 20th 2007, 10:41 AM
AfterShock
Quote:

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
• Jan 20th 2007, 10:48 AM
AfterShock
Quote:

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
• Jan 20th 2007, 10:55 AM
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.)
• Jan 20th 2007, 07:06 PM
AfterShock
Quote:

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