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Ray Of Light [21]
3 years ago
5

A family of four had dinner together at a restaurant. Write two expressions for calculating their total bill if they leave a 15%

tip. Let c represent the cost of their meal before tipping.
Mathematics
1 answer:
zavuch27 [327]3 years ago
3 0

Expression of total bill is t = 1.15c where t represents total bill and c represents cost of the meal before tipping.

<u>Solution:</u>

Given that family of four had dinner together at restaurant.

Percentage of tip left by family = 15%

Cost of the meal before tipping is represented by variable c.

Need to determine expression for total bill paid.

Let’s assume total bill be represented by variable t.

total bill = cost of the meal before tipping + 15% of tip

15% of tip means 15% of cost of meal before tipping.

=> <em>Total bill = cost of the meal before tipping + 15% of cost of meal before tipping. </em>

 On substituting given variable c and assumed variable t in above expression, we get

t = c + 15% of c

\begin{array}{l}{\Rightarrow t=c+\frac{15}{100} c} \\\\ {\Rightarrow t=\frac{100 c+15 c}{100}=\frac{115 c}{100}} \\\\ {\Rightarrow t=1.15 \mathrm{c}}\end{array}

Hence required expression of total bill is t = 1.15c where t represents total bill and c represents cost of the meal before tipping.

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Answer:

1) b =

\frac{13}{3}

2)m = -2.5

3)y = 15

4)x=2

Step-by-step explanation:

  1. subtract 8b from both sides
  2. subtract 2 from both sides
  3. divide both sides by 3
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2)Simplifying

7m + 32 = 12 + -1m

Reorder the terms:

32 + 7m = 12 + -1m

Solving

32 + 7m = 12 + -1m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add 'm' to each side of the equation.

32 + 7m + m = 12 + -1m + m

Combine like terms: 7m + m = 8m

32 + 8m = 12 + -1m + m

Combine like terms: -1m + m = 0

32 + 8m = 12 + 0

32 + 8m = 12

Add '-32' to each side of the equation.

32 + -32 + 8m = 12 + -32

Combine like terms: 32 + -32 = 0

0 + 8m = 12 + -32

8m = 12 + -32

Combine like terms: 12 + -32 = -20

8m = -20

Divide each side by '8'.

m = -2.5

Simplifying

m = -2.5

3)Simplifying

16 + -5y = 1 + -4y

Solving

16 + -5y = 1 + -4y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '4y' to each side of the equation.

16 + -5y + 4y = 1 + -4y + 4y

Combine like terms: -5y + 4y = -1y

16 + -1y = 1 + -4y + 4y

Combine like terms: -4y + 4y = 0

16 + -1y = 1 + 0

16 + -1y = 1

Add '-16' to each side of the equation.

16 + -16 + -1y = 1 + -16

Combine like terms: 16 + -16 = 0

0 + -1y = 1 + -16

-1y = 1 + -16

Combine like terms: 1 + -16 = -15

-1y = -15

Divide each side by '-1'.

y = 15

Simplifying

y = 15

4)Simplifying

2x + -8x + 1 = 9 + -10x

Reorder the terms:

1 + 2x + -8x = 9 + -10x

Combine like terms: 2x + -8x = -6x

1 + -6x = 9 + -10x

Solving

1 + -6x = 9 + -10x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10x' to each side of the equation.

1 + -6x + 10x = 9 + -10x + 10x

Combine like terms: -6x + 10x = 4x

1 + 4x = 9 + -10x + 10x

Combine like terms: -10x + 10x = 0

1 + 4x = 9 + 0

1 + 4x = 9

Add '-1' to each side of the equation.

1 + -1 + 4x = 9 + -1

Combine like terms: 1 + -1 = 0

0 + 4x = 9 + -1

4x = 9 + -1

Combine like terms: 9 + -1 = 8

4x = 8

Divide each side by '4'.

x = 2

Simplifying

x = 2

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