algebra Word problem

Question

The baseball team collected 2.5 times as many pounds of paper as the softball and soccer teams did together. The soccer team collected 50 pounds of paper. If all three teams collected 490 pounds of paper, how much did the softball team collect? how much did the baseball team collect?

Answer 1

x = pounds of paper the baseball team collected

y = pounds of paper the softball team collected

z = pounds of paper the soccer team collected

 

 

Let's write a system of equations to model this situation:

 

x = 2.5(y + z)        (baseball team collected 2.5 times softball and soccer teams together)

z = 50        (soccer team collected 50)

x + y + z = 490        (the three teams collected 490 together)

 

 

Plug z = 50 into the other two equations to get a system of two equations:

 

x = 2.5(y + z)

x = 2.5(y + 50)

x = 2.5y + 125

 

x + y + z = 490

x + y + 50 = 490

x + y = 440

 

 

Now, plug that first equation (x = 2.5y + 125) into the second equation and solve for y:

 

x + y = 440

2.5y + 125 + y = 440

3.5y + 125 = 440

3.5y = 315

y = 90

 

 

Finally, plug y = 90 back into the first equation to find x:

 

x = 2.5y + 125

x = 2.5(90) + 125

x = 225 + 125

x = 350

 

 

So, the baseball team collected x = 350 pounds and the softball team collected y = 90 pounds.