At avery middle school, 273 students responded to a survey asking whether a bulldog, a lion, or a tiger should be a new school mascot. four times as many students chose tiger. twice as many students chose lion as chose tiger. how many students chose lion?
a) 39 students
b) 78 students
c) 156 students
d) 273 students

Answer with Step-by-step explanation:

273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot.

Let t students chose tiger

b students chose bulldog

and l students chose lion

then, t+b+l=273

Four times as many students chose Bulldog as chose Tiger.

i.e. b=4t

Twice as many students chose Lion as chose Tiger.

i.e. l=2t

So, t+4t+2t=273

i.e. 7t=273

Dividing both sides by 7, we get

t=39

Number of students who chose lion=2t

                                                           = 2×39

                                                           = 78

Hence, Correct option is:

B) 78 students

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt