need help with percentages and fractions

[ceecil1959]

Could somebody help with this problem?

1. For last weeks science meet, 25% of the competitors were scheduled to be Seniors, but at the last moment, 4 underclassmen did not show up. If 31.25% of the actual competitors were seniors, how many seniors were in the meet?.

 

[Deleted member 4993]

Could somebody help with this problem?

1. For last weeks science meet, 25% of the competitors were scheduled to be Seniors, but at the last moment, 4 underclassmen did not show up. If 31.25% of the actual competitors were seniors, how many seniors were in the meet?.

The question is:

how many seniors were in the meet? ........................... Let's name the "FIND"

assume:

# of seniors were in the meet = S

# of underclassmen were in the meet = U

Total # of competitors in the meet =T

So we have:

T = S + U .................................and

25% of the competitors were scheduled to be Seniors .............................. → S = 0.25 * T .................................. (1)

When 4 underclassmen did not show up then:

New Total # of competitors in the meet =T - 4 .......................and

31.25% of the actual competitors were seniors ............................→ S = 0.3125 * (T-4) .........................................(2)

We have two equations and two unknowns. Solve ..............

 

[ceecil1959]

The question is:

how many seniors were in the meet? ........................... Let's name the "FIND"

assume:

# of seniors were in the meet = S

# of underclassmen were in the meet = U

Total # of competitors in the meet =T

So we have:

T = S + U .................................and

25% of the competitors were scheduled to be Seniors .............................. → S = 0.25 * T .................................. (1)

When 4 underclassmen did not show up then:

New Total # of competitors in the meet =T - 4 .......................and

31.25% of the actual competitors were seniors ............................→ S = 0.3125 * (T-4) .........................................(2)

We have two equations and two unknowns. Solve ..............

Thank you so much for your help. And for articulating it so well.

 

[HallsofIvy]

For some reason, I kept reading "upperclassman" instead of "underclassman" and got myself completely confused!

 

[Deleted member 4993]

For some reason, I kept reading "upperclassman" instead of "underclassman" and got myself completely confused!

I did that too - till and until the answer did not make sense. Finally light came on...

That is one of the reason - I gave a bit detailed response to this problem (kind of mia culpa )....