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A scientist mixed three chemicals, $R$ , $S$ , and $T$ , in a glass container. The amount of $R$ is $3$ times the amount of $S$ , and the amount of $T$ is $(1)/(6)$ the amount of $S$ . What is the ratio of the amount of $R$ to the amount of $T$ ? $\newline$ E. $S$ $1$ $\newline$ F. $S$ $2$ $\newline$ G. $S$ $3$ $\newline$ H. $S$ $4$

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Scale drawings: word problems

Full solution

Q. A scientist mixed three chemicals,

R

,

S

, and

T

, in a glass container. The amount of

R

is

3

times the amount of

S

, and the amount of

T

is

(1)/(6)

the amount of

S

. What is the ratio of the amount of

R

to the amount of

T

?

\newline

E.

S

1

\newline

F.

S

2

\newline

G.

S

3

\newline

H.

S

4

Denote Amounts: Let's denote the amount of S as ' $s$ '. According to the problem, the amount of R is $3$ times the amount of S, so we can write R as $3s$ . The amount of T is $(1/6)$ times the amount of S, so we can write T as $(1/6)s$ .
Express R and T: Now, we need to find the ratio of R to T. We can write this ratio as $R:T$ . Substituting the expressions for $R$ and $T$ in terms of $s$ , we get $(3s):(\frac{1}{6}s)$ .
Find Ratio: To simplify the ratio, we can divide both parts of the ratio by $s$ . This gives us $3:(1/6)$ .
Simplify Ratio: To further simplify, we can multiply both parts of the ratio by $6$ to get rid of the fraction. This gives us $(3\times6):(\frac{1}{6}\times6)$ , which simplifies to $18:1$ .

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