Word problem

Question

There are 7000 middle school students in four schools. There are three times as many students at Hill than at Bell. There are twice as many at Ware than at Bell. Cane had 176 more students than Ware. How many students are in each school?

Answer 1

Hello Bridget,

We can set up the following with the information given in the problem: 

Hill          s s s 
Bell          s
Ware       s s 
Cane        s s 176


The total of these four equal 1700, correct? 

Therefore: 

3s + s + 2s + 2s + 176 = 7000     <-----------------------------  I simply plugged all values into the equation from above


Simplify: 

8s + 176 = 7000 

Solve for s 

8s = 6824 

s  = 853


From the matrix that I made above we KNOW Bell has 853 students, correct? 

Solve for the other schools now, by plugging the value of 853 into the equations. 

Hill

3s 
3(853) = 2559

Ware 

2s
2(853) = 1706

Cane 

2s + 176 
2(853) + 176 = 1706 + 176
1882 

Summary of School attendees: 

Hill       = 2559
Bell      =   853
Ware    = 1706
Cane    = 1882

Sum of four school numbers: 


2559 + 853 + 1706 + 1882 = 7000

I hope I have helped and you understand. Please have a nice day tomorrow. 

Answer 2

H = 3*B

W = 2*B

C = 176 + W

H + B + W + C = 7000

You'll need to do some substitution until you have one equation with just one variable, which you can then solve. Then use that to plug into the other equations to find the values of the other variables.

(Hint: Try to set everything in the last equation in terms of B.)