Question

Seamus has $3$ times as many marbles as Ronit, and Taj has $7$ times as many marbles as Ronit. If Seamus has $s$ marbles then, in terms of $s$, how many marbles do Seamus, Ronit and Taj have together?

• A. $\frac{3}{7}s$
• B. $\frac{7}{3}s$
• C. $\frac{11}{3}s$
• D. $7s$
• E. $11s$

Answer 1

Answer: (C)

$\frac{11}{3}s$

The problem will be easier to solve if you can choose numbers that will give you all integers as you solve. both Seamus and Taj have a multiple of the number of marbles that Ronit has, so begin by picking for Ronit, not for Seamus.

If Ronit has $2$ marbles, then Seamus has $\left(3\right)\left(2\right)=6$ marbles and Taj has $\left(7\right)\left(2\right)=14$ marbles. Together, the three have $22$ marbles.

plug $s=6$ into the answer (remember that the problem asks about Seamus's starting number, not Ronit's and look for a match of $22$:

(A) $\frac{3}{7}s=$ not an integer

(B) $\frac{7}{3}s=\frac{7}{3}\left(6\right)=14$. Not a match

(C) $\frac{11}{3}s=\frac{11}{3}\left(6\right)=22$. Match!!

(D) $7s=42$. Not a match

(E) $11s=$ Too large

Alternately, you can use an algebraic approach. Begin by translating the first sentence into equations:

$s=3r$

$t=7r$

The question asks for the sum of the three:

$s+r+t=$?

The answer use only $s$, so figure out how to substitute to leave only $s$ in the equation

$r=\frac{s}{3}$

$t=7r=7\left(\frac{s}{3}\right)$

Substitute those into the equation

$s+r+t$

$s+\frac{s}{3}+7\left(\frac{s}{3}\right)$

$\frac{3s}{3}+\frac{s}{3}+\frac{7s}{3}$

$\frac{11s}{3}$

The correct answer is (C)