Answer to Question #303508 in Algebra for ERICKA

Question

Solve the following problems:

1. Jane and Albert bought a farm

measuring 78 3/5meters on one side, 63 7/10 meters on the second side, 132 5/9 meters on the third side, and 130 1/4 meters on the fourth side. The couple wants to fence the farm

with barbed wire. They have 2 rolls of barbed wire of 500 meters per roll on

hand. How many more meters of barbed wire would they have to buy if they want

to fence the farm four times?

2. Gabriela, Corazon and Remedios formed a partnership. Gabriela

contributed 1/2 of the capital. Corazon contributed 1/4 of what Gabriela contributed. Remedios contributed the remainder.

a. How much more did Gabriela

contribute than Corazon? Remedios?

b. Show the capital contributions

of the partners in terms of fractional parts.

c. Prove your answer in (b) using

subtraction.

d. If the total capitalization of

the partnership was 30 000.00, how much did each of the partners contribute?

Answer 1

1. The total length of the farm is 405.11 (78.6+63.7+132.56+130.25).

Since Jane and Albert want to fence the firm four times we will multiply the total length of the firm with 4 to find the total length that will be fenced.

405.11*4=1620.44

Jane and Albert have 1000 (500*2) metres of barbed wire.

To find the additional metres required, we will subtract the length of available barbed wire from the total length of the farm.

1620.44-1000=620.44

So Jane and Albert need an additional 620.44 metres to fence their farm four times.

2. Let's assume that the three partners contributed x amount in total.

So Gabriella will contribute 1/2x, Corazon contributed 1/4 of Gabriella's contribution, which is equal to 1/8x (1/4*1/2x), and Remedies contributed the rest, which is equal to 3/8x (1-1/8x-1/2x).

a. To find the amount that Gabriella contributed more than Corazon, we will subtract Corazon's contribution from Gabriella's

1/2x-1/8x=3/8x

So Gabriella contributed 3/8x more than Corazon.

To find the amount that Gabriella contributed more than Remedios, we will subtract Remedios's contribution from Gabriella's

1/2x-3/8x=1/8x

So Gabriella contributed 1/8x more than Remedios.

b. Capital contributions of the partners are shown below:

Gabriella: 1/2x

Corazon: 1/8x (1/4*1/2x)

Remedios: 3/8x (1-1/2x-1/8x)

c. We will first add the amount contributed by both Corazon and Remedios (1/8x+3/8x)= 1/2x

We will then subtract this figure from one to find Gabriella's contribution (1-1/2x)=1/2x

From the question, Gabriella had contributed half of the amount and this has been proven above

d. If the total contribution(x) was 30,000, then we will multiply this figure with the fractions given in b above

Gabriella: 1/2(30000)=15000

Corazon: 1/8(30000)=3750

Remedios: 3/8(30000)=11250