# Rebekah is going to leave a 20% tip for her meal. Let c represent the cost of her dinner. How do you write two expressions that can be used to calculate the cost of a dinner?

Jul 6, 2017

See the explanation.

#### Explanation:

Let the cost of the dinner without the tip be $c$
Let the total cost including the tip be $t$

The question does not state that the solution method is to be solved by simultaneous equations. In such a case you would expect wording on the lines of 'can be jointly used to calculate c'.

So we may use two slightly different forms of the same thing if we so wish.

$\textcolor{b l u e}{\text{Construct 1:}}$

$c + \frac{20}{100} c = t$

$c \left(1 + \frac{20}{100}\right) = t$

$c \left(\frac{100}{100} + \frac{20}{100}\right) = t$

$\frac{120}{100} c = t$

multiply both sides by $\frac{100}{120}$

$c = \frac{100}{120} t$

$c = \frac{5}{6} t \text{ } \ldots \ldots \ldots \ldots . E q u a t i o n \textcolor{w h i t e}{.} c o n s t r u c t \left(1\right)$

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$\textcolor{b l u e}{\text{Construct 2:}}$

We may construct a slightly different format by 'playing' around with the above.

6c=5t"".............Equation color(white)(.) construct (2)