I have 280 red and blue cups. 1/3 of the blue ones and 1/2 of the red ones are used at a party. If an equal amount of blue and red cups are used, how many were

Question

I can't figure out the solution. Can someone please explain it to me. Thanks. 

Answer 1

216 of each.

 

r + b=280

 

1/3b = 1/2r

 

solve top equation for r

r=280 -b

substitute

1/3b =1/2(280-b)

1/3b=140 -1/2b

5/6b=140

b=168   r=280-168=112

 

1/3(168)=56 blue   1/2(112)=56 red

Answer 2

r = number of red caps

b = number of blue caps

 

r + b = 280

b/3 = r/2

 

2b/3 = r             Substitute in top equation

 

2b/3 + b = 280

2b + 3b = 840

5b = 840

b = 168

 

You have 168 blue caps and 112 red caps.