Question

There were 50 more men than women at a concert on Day 1. On Day 2, thenumber of women decreased by 20% while the number of men remained thesame. Each concert ticket cost $108. There were 950 audience on Day 2. Howmuch money was collected from the sales of the concert tickets on both days?

Answer 1

Let's call X the number of women on day 1, Y the number of men on day 1, W the number of men on day 2, and Z the number of women on day 2.

There were 50 more men than women at a concert on Day 1, so:

Y = X + 50 eq.1

On Day 2, the number of women decreased by 20% while the number of men remained the same, so:

Z = (1-0.2)X = 0.8X eq. 2

Y = W eq. 3

There were 950 audiences on Day 2, so:

W + Z = 950 eq. 4

Now, we need to solve to find the value of X, Y, Z, and W.

So, we can start replacing W by Y on the last equation:

W + Z = 950

Y + Z = 950 eq. 5

Then, replacing eq. 2 and eq. 1 on eq. 5, we get:

Y + Z = 950

(X + 50) + (0.8X) = 950

Solving for X:

X + 50 + 0.8X = 950

1.8X = 950 - 50

X = 900/1.8

X = 500

If X is equal to 500, then, Y, W, and Z are equal to:

Y = X + 50 = 500 + 50 = 550

W = Y = 550

Z = 0.8X = 0.8(500) = 400

Finally, each concert ticket cost $108, so the money collected from the sales of the concert on both day was: