word problem help

Question

A third-grade teacher wants to plan a party for her school. She surveys her own class to find out their preference among chocolate cookies, ice cream sandwiches, and peanuts. Out of her 28 students, 12 prefer the cookies, 10 prefer the ice cream, and 6 prefer the peanuts. On the basis of this, how many of each dessert should she order for the 312 students at the school? (Assume that only whole cookies, ice cream sandwiches, and peanuts are sold. Round your answers up.)

Answer 1

This problem is about proportions.  A proportion is usually expressed as a fraction or a percent or as “a:b” and it represents the number in one group compared to the total number.

There are 28 students in this class.
    Prefer cookies  =   12/28
    Prefer ice cream  =  10/28
    Prefer peanuts  =  6/28

With proportion problems, don’t do calculations that you don’t have to do.  For example, don’t calculate what the above percentages are; let’s leave them as fractions for now.

For the entire school (population=312), we will assume that the same proportions exist.  So:
  Cookies     12/28 = C/3
                     28C = 3744      [cross multiply]
                  C = 133.7 rounded up is 134 cookies          [divide both sides by 28]

 Ice cream      10/28 =  I/312
                       28C = 8736      [cross multiply]
                    I = 111.4 rounded up is   112 ice cream     [divide both sides by 28]

  Peanuts     6/28 = P/312
                      28P = 1872      [cross multiply]
                      P = 66.9  rounded up is   67 Peanuts      [divide both sides by 28]

Just to check:
      Is 134 + 112 + 67  enough for 312 students ?   yes, it is 313

Answer 2

Using the data provided, we see that

12 of 28 students preferred cookies = 12/28 x 100% = 42.85%

10 of 28 students preferred ice cream = 10/28 x 100% = 35.71%

6 of 28 students preferred peanuts = 6/28 x 100% = 21.43%

 

We then will use those percentages to determine the purchases based on 312 students. So,

 

312 students x 42.85% = 312 x 0.4285 = 134 cookies

312 students x 35.71% = 312 x 0.3571 = 111 ice cream

312 students x 21.43% = 312 x 0.2143 =   67 peanuts