Problem Solving

3 teaspoons = 1 tablespoon
4 tablespoons = 1/4 cup

According to the information above, how many teaspoons are equal to 3/8 cup?

A. 3
B. 4
C. 9
D. 12
E. 18

Please explain....


I got this question correct by making an educated guess but need a little light on this problem..

Thanks.

Try backsolving
1/4 cup= 4tablespoon =>3/8 cup=3/2*1/4 cup=6 tablespoons.
Now, 1 tablespoon=3teaspoon, => 6 tablspn=18 tspn.

Is it clear?

Or you can you use algebra.

First step is to multiply 3 by 4 to get 12 tea spoons per 1/4 cup.

Then just set up an equation:

12/( 1/4 ) = x/( 3/8 ) [if there are 12 tea spoons in one-fourth of a cup, then how many tea spoons will there be in three-eigths of a cup]

First solve each side of the equal sign 12 * 4 = 48 and 8/3 * x = 8x/3

48 = 8x/3 [multiply both sides by 3]

144 = 8x [solve for x]

x = 18 I believe that this is quicker and is more intuitive than backsolving. Backsolving, however, is still a good way to go with some other problems when it is quicker than algebra.

dferm wrote:3 teaspoons = 1 tablespoon
4 tablespoons = 1/4 cup
According to the information above, how many teaspoons are equal to 3/8 cup?
A. 3
B. 4
C. 9
D. 12
E. 18
Please explain....

\[3\,\,{\text{teaspoons}}\,\,\,\, \leftrightarrow \,\,\,\,1\,\,\,{\text{tablespoon}}\]
\[4\,\,{\text{tablespoons}}\,\,\,\, \leftrightarrow \,\,\,\,\frac{1}{4}\,\,\,{\text{cup}}\,\,\,\,\,\]
\[\frac{3}{8}cup\,\,\, = \,\,\,\,?\,\,\,{\text{teaspoons}}\]
\[\frac{3}{8}cup\,\,\,\left( {\frac{{4\,\,{\text{tablespoons}}}}{{\frac{1}{4}\,\,\,{\text{cup}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\left( {\frac{{3\,\,{\text{teaspoons}}}}{{1\,\,\,{\text{tablespoon}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\frac{{3 \cdot 4 \cdot 4 \cdot 3}}{{8 \cdot 1}} = 18\,\,\,\,\,\,\,\,\,\left[ {{\text{teaspoons}}} \right]\]

This is a nice example of UNITS CONTROL technique, one of our most powerful tools!

(Arrows indicate licit converters.)

The above follows the notations and rationale taught in the GMATH method.