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Ali, Carrie and Bryan received a sum of money. Bryan's money was 3/5 as much as Ali's money. The ratio of Ali's money to Carrie'

monitta

Answer:

The sum of money received by Ali, Carrie and Bryan is $ 740.

Step-by-step explanation:

At first we translate mathematically each sentence:

(i) Ali, Carrie and Bryan received a sum of money.

$a$ - Ali's money.

$b$ - Bryan's money.

$c$ - Carrie's money.

(ii) Bryan's money was $\frac{3}{5}$ of Ali's money.

$b = \frac{3}{5}\cdot a$ (1)

(iii) The ratio of Ali's money to Carrie's money was 4 : 1.

$\frac{a}{c} = 4$ (2)

(iv) Ali had $ 160 more than Bryan.

$a = b + 160$ (3)

After some algebraic handling, we have the following system of linear equations:

$3\cdot a - 5 \cdot b = 0$ (1b)

$a - 4\cdot c = 0$ (2b)

$a - b = 160$ (3b)

The solution of the system is: $a = 400$ , $b = 240$ , $c = 100$

The sum of money is:

$s = a + b + c$

$s = 740$

The sum of money received by Ali, Carrie and Bryan is $ 740.

4 0

2 years ago

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c

Alenkasestr [34]

Step-by-step explanation:

this is the answer key for that question and etc...

4 0

3 years ago

What single decimal multiplier would you use to increase by 18% followed by a 12% decrease?

ValentinkaMS [17]

Answer:

The single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

Step-by-step explanation:

Let 'x' be the number

As first the number has to be increased by 18%

so

Step 1: write the percentage '18%' in decimal form

18% = 0.18

Step 2: For percentage increases: add the decimal to 1

1 + 0.18 = 1.18

Step 3: Multiply the number x by the multiplier, found in Step 2

x × 1.18 = 1.18x

NEXT WE HAVE TO DECREASE 1.18x by 12%

Apply the same method but with a number 1.18x

Write the percentage '12%' in decimal form

12% = 0.12

For percentage decreases: subtract the decimal to 1

1 - 0.18 = 0.18

Multiply the number 1.18x by the multiplier, found in Previous step

1.18x × 0.18 = 0.21x

Therefore, the single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

7 0

2 years ago

Round 48.078 to the nearest tenth

nasty-shy [4]

Answer:

50

Step-by-step explanation:

48 rounds to 50

ANSWER: 50

6 0

2 years ago

Read 2 more answers

Jasmine had a carrot cake with cream cheese frosting for her birthday .she and her friend each ate 1/4 of the cake and jasmine's

zloy xaker [14]

Hey there!

To solve this problem, you first would need to solve for how much of the cake is left after Jasmine, her friend, and Jasmine's brother got their slices. Then, you would need to split the remaining amount in half to get the answer of what each parent ate. We would need to make all of the denominators the same, so let's make all of the fractions out of 12, a common denominator of 3 and 4.

$\frac{12}{12} - \frac{1}{4} - \frac{1}{4} - \frac{1}{3}$
$\frac{12}{12} - \frac{3}{12} - \frac{3}{12} - \frac{4}{12}$
$\frac{12}{12} - \frac{10}{12} = \frac{2}{12}$

It can then be concluded that each parent ate $\frac{1}{12}$ of the cake, since there was $\frac{2}{12}$ remaining.

You can check this answer by adding up all of the parts we used in this problem:

$\frac{3}{12} + \frac{3}{12} + \frac{4}{12} + \frac{1}{12} + \frac{1}{12} = \frac{12}{12}$

Hope this helped you out! :-)

3 0

2 years ago