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elena-14-01-66 [18.8K]
3 years ago
5

The Country Buffet restaurant has tables that seat 6 people and booths that can seat 4 people. The restaurant has 38 seating uni

ts for seating a total of 188 people. Write a system of equations and use it to find the number of tables and the number of booths that are at the restaurant?
Define your variables for this system.
Mathematics
1 answer:
Alina [70]3 years ago
6 0

Answer:

There are 20 booths and (38 - 20), or 18, tables

Step-by-step explanation:

Represent the number of tables with t and the number of booths with b.

We need to find the values of t and b.

(6 people/table)(t) + (4 people/booth)b = 188           (units are "people")

t + b = 38                                                                      (units are "seating units")

Solving the second equation for t, we get 38 - b = t.

Substitute 38 - b for t in the first equation:

(6 people/table)(38 - b) + (4 people/booth)b = 188

Then solve for b:   6(38) - 6b + 4b = 188, or:

228 - 2b = 188, or 2b = 228 - 188, or 2b = 40.  Thus, b = 20   (booths)

There are 20 booths and (38 - 20), or 18, tables.

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Answer:

\huge{ \fbox{ \sf{ - 2y - 30}}}

Step-by-step explanation:

\star{ \sf{ \: (4y - 10) - (6y + 20)}}

\text{Step \: 1 }\:  :  \sf{While \: subtracting \: sign \: of \: each \: term \: of \: the \: second \: expression \: changes}

\hookrightarrow{ \sf{4y - 10 - 6y - 20}}

\text{Step \: 2 \:  :  \sf Collect \: like \: terms}

\sf{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}

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\hookrightarrow{ \sf{ - 2y - 10 - 20}}

\text{Step \: 3 \:  :  \sf{Calculate}}

\underline{ \text{Remember!}}  :  \sf{The \: negative \: integers \: are \:always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}

\hookrightarrow{ \sf{ - 2y - 30}}

Hope I helped!

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3 years ago
Does anybody know the answers to these? will mark brainliest!
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Answer:

1.

Tan 45=√2/n

n=√2

again

sin 45=√2/m

m=2

answer:<u> </u><u>m</u><u>=</u><u>2</u><u>,</u><u>n</u><u>=</u><u>√</u><u>2</u>

<u>2</u><u>.</u>

sin 45=x/3

x=3/√2=3√2/2

y=3√2/2

<u>a</u><u>n</u><u>s</u><u>:</u><u>x</u><u>=</u><u>3√2/2</u><u>,</u><u>y</u><u>=</u><u>3√2/</u><u>3</u>

<u>3</u><u>.</u>

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ans:<u>a</u><u>=</u><u>4</u><u>/</u><u>√</u><u>2</u><u>,</u><u>b</u><u>=</u><u>4</u><u>/</u><u>√</u><u>2</u>

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b=4 base sides of isosceles triangle

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ans:<u>a</u><u>=</u><u>4</u><u>√</u><u>2</u><u> </u><u>and</u><u> </u><u>b</u><u>=</u><u>4</u>

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