A theater can seat 294 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?

Question

seriously, have no clue how to do this ish. 

Answer 1

A theater can seat 294 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?

 

Say, there are R rows in theater. Then, in each row there are S=R+7 seats (seats are more than rows ...)

 

Total number of seats is R*S and it is 294. That is:

 

R*(R+7)=294

R^2+7R-294=0

Solving quadratic equation:

 

R=(-7+-sqrt(49+4*294))/2=(-7+-35)/2=(-7+35)/2=14

 

R=14 !!!

                           [and S=21, and # of seats is 21*14=294]

Answer 2

Let's say that the number of seats in each row is S. That means that the number of rows is S-7. The number of seats is the number of seats in a row multiplied by the number of rows. Here, that is S*(S-7). The problem tells you that the number of seats is 294, so S*(S-7)=294. From here, you could solve the equation for S.

 

Another option is to think about how the numbers are working together. Two numbers, which are 7 apart, multiply together to make 294.

 

Notice the 4 in the ones place. That tells you that the ones places of the two numbers must be something that gives you a 4 in the ones place of the product. That could be 1x4, 2x7, or 3x8.

 

Also, you could notice that 20x20=400 is too high, and 15x15=225 is too low, so the numbers that you are looking for are around the upper teens. Now, you have it narrowed down to three options because you know what numbers are in the ones place. The 1x4 option could give you 21x14. That is 7 apart. No other combination is 7 apart, so that has to be the answer. Now, double checking with a calculator, 21x14=294, so that's it.

 

But, which is which? The bigger number is seats in a row, so that's 21. The only possibility for number of rows is now 14.