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3 years ago

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A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together

to make the 60% solution.
Let x represent the number of liters of the 50% solution.
Let y represent the number of liters of the 90% solution.
Which equation represents the total liters of acid that are needed?
Question 3 options:
x + y = 6
x + y = 10
0.5x + 0.9y = 6
0.5x + 0.9y = 10

1 answer:

sineoko [7]3 years ago

6 0

Answer:

<u>The equations system is:</u>

<u>x + y = 10</u>

<u>0.5x + 0.9y = 6</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Liters of 60% acid solution needed = 10

x = Number of liters of the 50% solution

y = Number of liters of the 90% solution

2. Which equation represents the total liters of acid that are needed?

There are two equations needed:

The first one related to the total liters needed, 10 in this case:

x + y = 10

The second one related to the acid concentration of the 10 liters:

0.5x + 0.9y = 10 * 0.6

0.5x + 0.9y = 6

<u>The equations system is:</u>

<u>x + y = 10</u>

<u>0.5x + 0.9y = 6</u>

Solving for x and y in the 2nd equation, we have:

0.5 (10 - y) + 0.9y = 6

5 - 0.5y + 0.9y = 6

0.4y = 6 - 5

0.4y = 1

y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)

The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.

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Question:

The quantities x and y are in proportion

x y

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(a) Find the values of a and b.

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Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

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The equation is then calculated using:

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Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

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Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

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Solving (b): The constant of variation.

This has been solved in (a) above as:

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From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

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