8.11: Fruit Confusion
Fruit Confusion – Reason Proportionally
Teacher Notes
In each problem, students are presented with a box of fruit labeled with it weight or cost, and a sign giving the cost for one or more pounds of the fruit or the cost of two or more pieces of the fruit. The pieces of fruit are of the same type (eg., all bananas) and are countable. Students use a proportion to figure out the average weight or cost of one piece of fruit. Students may use calculators for the computations.
Solutions

\begin{align*}\$0.14; \frac{\$ 0.69}{1\ pound} = \frac{x \ dollars}{1.2\ pounds}\end{align*}
$0.14;$0.691 pound=x dollars1.2 pounds , so \begin{align*}x\end{align*}x is about $0.83. One orange is \begin{align*}\$0.83 \div 6\end{align*}$0.83÷6 or about $0.14. 
\begin{align*}\$3.60; \frac{9 \ pounds}{x \ dollars} = \frac{4 \ avocados}{\$ 2.40}\end{align*}
$3.60;9 poundsx dollars=4 avocados$2.40 , so \begin{align*}x = \$5.40\end{align*}x=$5.40 , the cost of 1.5 pounds. The cost of one pound is \begin{align*}\$5.40 \div 1.5\end{align*}$5.40÷1.5 , or $3.60.  0.7 pounds; \begin{align*}\frac{2\ pounds}{\$ 1.00} = \frac{x \ pounds}{\$ 2.10}\end{align*}
2 pounds$1.00=x pounds$2.10 , so \begin{align*}x = 4.2\end{align*}x=4.2 pounds. One grapefruit weighs \begin{align*}4.2 \div 6\end{align*}4.2÷6 , or about 0.7 pounds. 
\begin{align*}\$0.05; \frac{3\ pounds}{\$ 1.20} = \frac{1.5\ pounds}{x \ dollars}\end{align*}
$0.05;3 pounds$1.20=1.5 poundsx dollars , so \begin{align*}x = \$0.60\end{align*}x=$0.60 , and \begin{align*}\$0.60 \div 12 = \$0.05\end{align*}$0.60÷12=$0.05 .
\begin{align*}& \mathbf{Describe:} && \text{There are}\ 8\ \text{bananas in a box weighing a total of}\ 3.2\ \text{pounds. A sign shows that}\\ & && 4\ \text{pounds of bananas cost}\ \$2.00. \\ \\ & \mathbf{My \ Job:} && \text{Figure out the cost of one banana. Assume bananas weigh the same.} \\ \\ & \mathbf{Plan:} && \text{Use a proportion to figure out the cost of}\ 3.2\ \text{pounds of bananas}. \\ & && \text{Then divide that cost by 8 to get the cost of one banana}. \\ \\ & \mathbf{Solve:} && \frac{4\ pounds}{\$ 2.00} = \frac{3.2\ pounds}{x \ dollars}; 4x = \$2.00 \times 3.2.\ \text{So},\ 4x = \$6.40,\ \text{and}\ \$6.40 \div 4 = \$1.60. \\ & && \text{One banana costs}\ \$1.60 \div 8,\ \text{or}\ \$0.20. \\ \\ & \mathbf{Check:} && \text{One banana weighs}\ 3.2 \div 8,\ \text{or}\ 0.4\ \text{pounds and costs}\ \$0.20. \\ & && 10\ \text{bananas} \times 0.4\ \text{pounds/banana} = 4\ \text{pounds}. \\ & && 10\ \text{bananas} \times \$0.20/\text{banana} = \$2.00\end{align*}