Question

After a long Saturday soccer match. Stadio soccer players decided to go to a local restaurant for a meal. They agreed to equally split the total cost of the meal. After everything was eaten, the cost, amounting to R28.80, arrived at the table. Three of the players noticed that they had left their cash at home. However, the remaining players agreed to pay R0.80 more to cover the missing amount. How many players were originally going to pay for this meal?

Answer 1

Let $x$ denotes the number of players. Then we have the equation $\frac{28.8}{x}+0.8=\frac{28.8}{x-3}.$ It follows that $\frac{28.8+0.8x}{x}=\frac{28.8}{x-3}$, and hence $(28.8+0.8x)(x-3)=28.8x$. We have the equation $0.8x^2-2.4x-86.4=0$ which is equivalent to $x^2-3x-108=0$, and hence $(x-12)(x+9)=0$. Taking into account that $x>0$, we conclude that the number of players is $x=12.$