Typical "fencing" problem.

[Jaskaran]

hey all, I'm doing a review of basic algebra, and I seem to be lost in this problem.

"Clint is constructing two adjacent rectangular dog pens. Each pen will be three times as long as it is wide, and the pens will share a common long side. If Clint has 65 ft of fencing, what are the dimensions of each pen?"

My first approach was to make a diagram, etc.

I know P = 2L + 2W

So if the length (L) = 3w, then 65 ft = 2(3w) + 2w ?

I get W as 8.125.

Obviously this isn't correct, the book says that the sides are 5ft by 15ft (makes sense, 15 is three times 5)

Then, I have this problem:
"Brent lent his brother Bob some money at 8% simple interest, and he lent his sister Betty half as much money at twice the interest rate. Both laons were for one year (is this significant in the problem?). If Brent made a total of 24 cents in interest, then how much did he lend to each one?"

I'm thinking that:

x + .08x = Bob

.5x + .16x = Betty.

But how do I solve for (x - 24 cents)?

Any help?

Thanks =]

 

[Deleted member 4993]

hey all, I'm doing a review of basic algebra, and I seem to be lost in this problem.

"Clint is constructing two adjacent rectangular dog pens. Each pen will be three times as long as it is wide, and the pens will share a common long side. If Clint has 65 ft of fencing, what are the dimensions of each pen?"

My first approach was to make a diagram, etc.

I know P = 2L + 2W <<< For two "length by length" joined pens P = 3L + 4W

So if the length (L) = 3w, then 65 ft = 2(3w) + 2w ?

I get W as 8.125.

Obviously this isn't correct, the book says that the sides are 5ft by 15ft (makes sense, 15 is three times 5)

Then, I have this problem:
"Brent lent his brother Bob some money at 8% simple interest, and he lent his sister Betty half as much money at twice the interest rate. Both laons were for one year (is this significant in the problem? sure it is - think about it - would he make more money if he had lent money for 2 years?). If Brent made a total of 24 cents in interest, then how much did he lend to each one?"

I'm thinking that:

x + .08x = Bob
What is 'x'?
.5x + .16x = Betty.

Let us assume

Bob borrowed = x dollars

Betty borrowed = 0.5 x dollars

then

interest earned from Bob = 0.08 * x

interest earned from Betty = 0.16 * 0.5x = 0.08 * x

so total earned

0.08 x + 0.08 x = 0.24

Now solve for 'x'

But how do I solve for (x - 24 cents)?

Any help?

Thanks =]

 

[Loren]

Draw a rectangle. That represents one pen. Label the short side "w". Label the long side "3w". Draw the second rectangle such that one of its long sides is common with the original rectangle. Label all the unlabeled sides in accordance with the existing labels on the original rectangle (the short sides are labeled w and the long sides are labeled 3w). Now, look at what you have. Write your equation on the basis that the sum of all the sides (there are 7 of them, 4 short sides and 3 long sides) add up to 65.