The total number of football (x) and basketball (y) is 180. There are 30 more football than basketball. How many of each basketball and football are there?
The total number of football (x) and basketball (y) is 180 mean:
x + y = 180
There are 30 more football than basketball mean:
x = y + 30
Replace this value in equation x + y = 180
x + y = 180
y + 30 + y = 180
2 y + 30 = 180 Subtract 30 to toth sides
2 y + 30 - 30 = 180 - 30
2 y = 150 Divide both sides by 2
y = 150 / 2
y = 75
x = y + 30 = 75 + 30 = 105
Football 105
Basketball 75
To solve this problem, we can set up a system of equations based on the given information.
Let's assign variables to the number of footballs and basketballs.
Let x represent the number of footballs, and y represent the number of basketballs.
Based on the given information, we have two equations:
1) The total number of footballs and basketballs is 180:
x + y = 180
2) There are 30 more footballs than basketballs:
x = y + 30
Now, we can use these equations to find the values of x and y.
Substitute equation 2) into equation 1) to eliminate x:
(y + 30) + y = 180
Combine like terms:
2y + 30 = 180
Subtract 30 from both sides of the equation:
2y = 150
Divide both sides by 2:
y = 75
Now, substitute y = 75 back into equation 2) to find the value of x:
x = y + 30
x = 75 + 30
x = 105
Therefore, there are 105 footballs and 75 basketballs.