Question

If 280 oranges are divided among 50 girls and boys so that each boy gets 5 oranges and each girl gets 7 oranges, how many girls are there?

Answer 1

Let's assume there are "x" girls and "y" boys.

According to the given information, the total number of oranges is 280.

So we can set up two equations:

1. Total oranges equation: 7x (oranges for each girl) + 5y (oranges for each boy) = 280 (total oranges)

2. Total children equation: x (number of girls) + y (number of boys) = 50 (total children)

Now we can solve these two equations simultaneously to find the values of "x" and "y."

Let's solve the first equation for "y": 5y = 280 - 7x y = (280 - 7x) / 5

Now, we'll substitute the value of "y" from the above equation into the second equation:

x + (280 - 7x) / 5 = 50

Now, we'll solve for "x":

5x + 280 - 7x = 250 -2x = -30 x = 15

Now that we have the value of "x," we can find the value of "y":

y = (280 - 7 * 15) / 5 y = (280 - 105) / 5 y = 175 / 5 y = 35

So, there are 15 girls and 35 boys in the group.