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3 years ago

5

Wayne and Garth are planning to have a concert. They have found two good options. Option 1: Malcolm's Music Hall will pay them $

100 for playing and add $15 per person in the audience. Option 2: Reggie's Reggae Room will pay them $350 for playing and add 10$ per person in the audience.

1 answer:

storchak [24]3 years ago

8 0

Answer:

50 people

Step-by-step explanation:

If you are to calculate the number of people that will come to the concert that will ensure option 1 and option 2 to yield equal amount

Let

x = number of people

Option 1:

Malcolm's Music Hall = 100 + 15x

Option 2:

Reggie's Reggae Room = 350 + 10x

Equate both options

100 + 15x = 350 + 10x

Collect like terms

100 - 350 = 10x - 15x

-250 = - 5x

x = -250/-5

x = 50 people

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Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul

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Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, $18 inches = 1.5 ft$

Thus, the length of the rug is $l=1.5+w$

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

$A=length\times width$

$10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0$

Solving the expression using the quadratic formula,

$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values, we have,

$$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\$

$w=\frac{-15 \pm \sqrt{4225}}{20}$

$w=\frac{-15 \pm 65}{2 0}$

Thus,

$w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5$ and $w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4$

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

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Thus, the length of the rug is 4 ft.

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Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

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$\boxed{ \mathfrak { question↷}}$

Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

$\boxed{ \mathfrak { solution↷}}$

Let Pip get be x and fiona get be x+35

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$\tt \frac{x + 35}{x } = 6$

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