Question

Can someone please help I need a clear explanation on how to solve this equation.

At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?

Answer 1

b = amount of students who chose Bulldog

n = amount of students who chose lion

t = amount of students who chose tiger

so.. "t" chose tiger, ok

"Four times as many students chose Bulldog as chose Tiger"
namely, if "t" chose tiger, then 4 times that many chose Bulldog, thus

b = 4t

"Twice as many students chose Lion as chose Tiger"
namely, if "t" students chose tiger, twice as many chose lion

n = 2t

now, we know a total of 273 students were surveyed, thus


`\bf \begin{cases} b+n+t=273\\ \boxed{4t}+\boxed{2t}+t=273 \end{cases} \\\\\\ 7t=273\implies t=\cfrac{273}{7}\impliedby \textit{that many chose \underline{tiger}}`

Answer 2

78 students chose lion.

Explanation:

Let x students chose tiger.

Let y students chose bull dog.

Let z students chose lion.

Total students = 273

`x+y+z=273` ....(1)

Four times as many students chose Bulldog as chose Tiger.

`y=4x`

Twice as many students chose Lion as chose Tiger.

`z=2x`

Substituting the values of y and z in (1)

`x+4x+2x=273`

=>
`7x=273`

x = 39 (students who chose tiger)

We have to find students who chose Lion or z (defined above)

`z=2x`

`z=2(39)`

So, z = 78

Therefore, 78 students chose lion.