2 Answers

Matt Houser · Answer 1 · 2023-06-12T18:48:30+0000

Lixin has x number of classmates and plan to buy her a birthday gift worth $36.

So basically, they need to contribute 36/x dollars each in order to buy the gift.

But 5 of them will not contribute and it cost them to add $0.24 each

So from 36/x dollars, it become (36/x + 0.24) dollars each

Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)

The equation will be :

$\begin{gathered} \text{contribution}*\text{ number of classmates}=36 \\ ((36)/(x)+0.24)(x-5)=36 \end{gathered}$

Simplify the equation :

$\begin{gathered} ((36)/(x)+0.24)(x-5)=36 \\ (36)/(x)(x-5)+0.24(x-5)=36 \\ (36-(180)/(x))+(0.24x-1.2)=36 \end{gathered}$

Multiply both sides by x to remove the denominator.

$\begin{gathered} x(36-(180)/(x))+x(0.24x-1.2)=36x \\ 36x-180+0.24x^2-1.2x=36x \end{gathered}$

Rearrange and combine like terms :

$\begin{gathered} 0.24x^2+36x-1.2x-36x-180=0 \\ 0.24x^2-1.2x-180=0 \end{gathered}$

Divide both sides by 0.24 to make the coefficient of x^2 become 1 :

$\begin{gathered} (0.24x^2)/(0.24)-(1.2x)/(0.24)-(180)/(0.24)=0 \\ x^2-5x-750=0 \end{gathered}$

Solve by factoring completely :

$\begin{gathered} x^2-5x-750=0 \\ (x-30)(x+25)=0 \end{gathered}$

Equate both factors to 0, then solve for x :

x - 30 = 0

x = 30

x + 25 = 0

x = -25

Neglect negative value since there is no negative value for the number of persons.

The answer is x = 30

To summarize :

i Expression in terms of x :

ii Equation in x that reduces to x^2 - 5x - 750 = 0

$\begin{gathered} 0.24x^2-1.2x-180=0 \\ \Rightarrow x^2-5x-750=0 \end{gathered}$

iii Number of classmates Lixin has.

x = 30

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