In a survey, the ratio of students who prefer pizza to chicken nuggets is 2 : 5. If 357 students were surveyed, how many prefer pizza?

Question

I dont really understand this question. 

Answer 1

We will look at the ratios as follows.  Let's assign the following values...

 

P=Pizza

C=Chicken

T=Total

 

P:C :: 2:5........ratio, pizza to chicken, given

P+C = 2+5 = 7 total

 

Rewrite the ratio as "pizza (P) to total (T)".  So....

P:T :: 2:7 :: P:357

 

We can rewrite the ratios as fractions...

 P         2          P

---  =   ----  =  ------

 T         7        357

 

Now cross-multiply and solve for "P"...

  7P=2(357)

  7P=714

∴ P=102 students

 

So 102 students prefer pizza.

 

Repeat the same ratio, equation setup for the ratio "C:T" (chicken to total).  I will let you show the work.  You should arrive at a value of "C=255 students".  Let's check our work...

 

         P+C=357....given, problem statement

102+255=357....substitute for "P and C", simplify

         357=357....true, √check, our values are

                             correct.

 

Always check your solutions and work!