Let's denote the number of soccer club members as x.

The initial cost per person is $192/x.

When 2 more students join the trip, the total number of people becomes x+2 and the cost per person drops to $192/(x+2).

According to the problem, the initial cost per person is $3.20 more than the cost per person after the 2 students join. So we can set up the following equation:

192/x = 192/(x+2) + 3.20

To solve this equation, we first multiply all terms by x(x+2) to get rid of the denominators:

192(x+2) = 192x + 3.20x(x+2)

Expanding and simplifying gives:

192x + 384 = 192x + 3.20x^2 + 6.40x

Subtract 192x from both sides:

384 = 3.20x^2 + 6.40x

Divide all terms by 3.20:

120 = x^2 + 2x

Rearrange into a standard quadratic equation:

x^2 + 2x - 120 = 0

Factor the equation:

(x - 10)(x + 12) = 0

Setting each factor equal to zero gives the solutions x = 10 and x = -12.

Since the number of people cannot be negative, the only valid solution is x = 10.

So, there are 10 soccer club members going to the tournament. The correct answer is B. 10.

Question

Let's denote the number of soccer club members as x.

The initial cost per person is $192/x.

When 2 more students join the trip, the total number of people becomes x+2 and the cost per person drops to $192/(x+2).

According to the problem, the initial cost per person is $3.20 more than the cost per person after the 2 students join. So we can set up the following equation:

192/x = 192/(x+2) + 3.20

To solve this equation, we first multiply all terms by x(x+2) to get rid of the denominators:

192(x+2) = 192x + 3.20x(x+2)

Expanding and simplifying gives:

192x + 384 = 192x + 3.20x^2 + 6.40x

Subtract 192x from both sides:

384 = 3.20x^2 + 6.40x

Divide all terms by 3.20:

120 = x^2 + 2x

Rearrange into a standard quadratic equation:

x^2 + 2x - 120 = 0

Factor the equation:

(x - 10)(x + 12) = 0

Setting each factor equal to zero gives the solutions x = 10 and x = -12.

Since the number of people cannot be negative, the only valid solution is x = 10.

So, there are 10 soccer club members going to the tournament. The correct answer is B. 10.

Knowee AI · Accepted Answer