Question

Ann, Bina and Cara share $66. The amount Ann and Bina get is in the ratio 9:5 The amount Bina and Cara get is in the ratio 2:1 How much does Ann get?

Answer 1

Ответ:

Let's assign variables to the amounts received by Ann, Bina, and Cara.

Let A be the amount Ann receives.

Let B be the amount Bina receives.

Let C be the amount Cara receives.

According to the given information, the amount Ann and Bina get is in the ratio 9:5. This can be expressed as:

A/B = 9/5

Similarly, the amount Bina and Cara get is in the ratio 2:1, which can be expressed as:

B/C = 2/1

We also know that the total amount shared is $66, so we have:

A + B + C = 66

To solve this system of equations, we can use substitution. From the second equation, we can express B in terms of C as:

B = (2/1)C

Now, substitute B in the first equation:

A / ((2/1)C) = 9/5

Multiply both sides of the equation by ((2/1)C):

A = ((2/1)C) * (9/5)

Simplifying the right side:

A = (18/5)C

Now substitute A and B into the third equation:

((18/5)C) + ((2/1)C) + C = 66

Multiply both sides of the equation by 5 to eliminate fractions:

18C + 10C + 5C = 330

Combine like terms:

33C = 330

Divide both sides of the equation by 33:

C = 330 / 33

C = 10

Now, substitute C = 10 back into the equations to find A and B:

A = (18/5)C = (18/5) * 10 = 36

B = (2/1)C = (2/1) * 10 = 20

Therefore, Ann receives $36

Answer 2

Let's denote the amount Ann gets as \(9x\), where \(x\) is a common multiplier. Since the ratio of Ann's to Bina's share is 9:5, the amount Bina gets is \(5x\). Similarly, the ratio of Bina's to Cara's share is 2:1, so the amount Cara gets is \(2x\).

Now, according to the information given, the sum of their shares is $66:

\[9x + 5x + 2x = 66\]

Combining like terms:

\[16x = 66\]

Now, solve for \(x\):

\[x = \frac{66}{16} = \frac{33}{8}\]

Now that we have the value of \(x\), we can find the amount Ann gets:

\[Ann's\ share = 9x = 9 \times \frac{33}{8} = \frac{297}{8}\]

So, Ann gets \(\frac{297}{8}\) dollars. If you prefer a decimal answer, it is approximately $37.13.