Question

At a fancy vegetable stand, Jim bought purple tomatoes for $ 8 $ each and Aubrey bought organic giant cabbages for $ 12 $ each. In total, they paid $ 104 $ for $ 10 $ vegetables. How many cabbages did Aubrey buy?
A.Three
B. Five
C. Six
D. Seven
E. Eight

Answer 1

Hint: Assume the number of tomatoes and Organic giant cabbages bought. Then form the equations according to given and solve the equations to find the number of tomatoes and organic giant cabbages.

Complete step-by-step answer:
Jim bought purple tomatoes for $ 8 $ each and Aubrey bought organic giant cabbages for $ 12 $ each. In total, they paid $ 104 $ for $ 10 $ vegetables.
Assume that the number of tomatoes bought by Jim are $ x $ and the number of organic giant cabbages bought by Aubrey are $ y $ .
The cost for $ x $ tomatoes is $ 8x $ as each tomato costs $ 8 $ and the cost for $ y $ organic giant cabbages is $ 12y $ as the cost for each organic giant cabbage is $ 12 $ .
The total cost of all the vegetables is $ 104 $ . So,
 $ 8x + 12y = 104\;\;\;\;\;\; \ldots \left( 1 \right) $
According to the condition the total number of vegetables is $ 10 $ . So,
 $ x + y = 10\;\;\;\;\;\;\;\; \ldots \left( 2 \right) $
Substitute the value of $ y $ from equation $ \left( 2 \right) $ in equation $ \left( 1 \right) $ .
 $
\Rightarrow 8x + 12y = 104 \\
\Rightarrow 8x + 12\left( {10 - x} \right) = 104 \\
\Rightarrow 8x + 120 - 12x = 104 \\
\Rightarrow 120 - 104 = 4x \;
  $
Further simplify,
 $
\Rightarrow 120 - 104 = 4x \\
\Rightarrow 4x = 16 \\
\Rightarrow x = \dfrac{{16}}{4} \\
\Rightarrow x = 4 \;
  $
Substitute the value of $ x $ in equation $ \left( 2 \right) $ for the value of $ y $ .
 $
\Rightarrow x + y = 10 \\
\Rightarrow 4 + y = 10 \\
\Rightarrow y = 10 - 4 \\
\Rightarrow y = 6 \;
  $
So, the number of cabbages bought was $ 6 $ .
So, the correct answer is “Option C”.

Note: Form the right equations with the conditions given in the question. Avoid calculation mistakes to avoid the confusion. Take care of the variable taken for each vegetable which makes confusion. Since there are two variables we need to have two or more equations to solve them.