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3 years ago

A hospital cafeteria has 20

Mathematics

2 answers:

Leno4ka [110]3 years ago

7 0

Answer:

<h2>There are 106 chairs in the hospital cafeteria.</h2>

Step-by-step explanation:

Givens

There are 20 tables.
65% of the tables have 6 chairs at each table.
35% of the tables have 4 chairs at each table.

The question is, what's the total number of chairs in the cafeteria?

We know by given that 100% represents 20 tables. We can use the rule of three, to find the number that represents a 65%, that is, if 100% is 20 tables, 65% how many tables would be?

$65\%\frac{20}{100\%} =13$

There are 13 tables of 6 chairs at each table.

Similarly, if 100% represents 20 tables, 35% how many tables would represent?

$35\%\frac{20}{100\%} =7$

There are 7 tables of 4 chairs at each table.

Then, we need to multiply to find the total number of chairs.

We know that there are 13 tables of 6 chairs, so

$13 tables \times 6 chairs=78 chairs$

We also know that there are 7 tables of 4 chairs, so

$7 tables \times 4chairs=28chairs$

Therefore, the total number of chairs is

$78+28=106$

There are 106 chairs in the hospital cafeteria.

Virty [35]3 years ago

6 0

Answer:

Step-by-step explanation:

So if their is 65% of 20 tables with 6 chairs that's 13 tables.

And if their is 35% of 20 tables with 4 chairs that's 7 tables.

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Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 33 ft long. She

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<h3>Answer: 16 ft by 25 ft</h3>

=========================================================

Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

Cynthia can afford to buy 400 sq ft of carpet

So we set 400 equal to that previous expression and solve for x

(24-2x)(33-2x) = 400

24(33-2x) - 2x(33-2x) = 400

792-48x - 66x + 4x^2 = 400

4x^2 - 114x + 792 = 400

4x^2 - 114x + 792-400 = 0

4x^2 - 114x + 392 = 0

From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\$