Practice Solutions

1. Russell bought half of all of the available bunches of bananas. The store had 14 bunches left. How many bunches of bananas did the store originally have?

b: bunches of bananas

$\begin{array}{rcl}\frac{1}{2}b& =& 14\\ \left(\frac{2}{1}\right)\frac{1}{2}b& =& 14\left(\frac{2}{1}\right)\\ b& =& 28\end{array}$              

The store originally had 28 bunches of bananas.

2. Donna bought three packages of strawberries and two pounds of grapes. The cost of one pound of grapes is $1.75. If Donna spent a total of $10.50, what is the cost of one package of strawberries? Round to the nearest cent. 

w: strawberries, g: grapes

$\begin{array}{rcl}3w+2g& =& 10.50\\ 3w+2\left(1.75\right)& =& 10.50\\ 3w+3.50& =& 10.50\\ & & –3.50 –3.50\\ \left(\frac{1}{3}\right)3w& =& 7\left(\frac{1}{3}\right)\\ w& =& \frac{7}{3}=2\frac{1}{3}\\ w& =& 2.33\end{array}$

One package of strawberries costs $2.33.

3. Tate is paid $12 per hour. If Tate has already saved $120, how many hours does he need to work to have a total of $360?

$\begin{array}{rcl}h& =& \mathrm{hours}\\ 12h+120& =& 360\\ & & –120 –120\\ \left(\frac{1}{12}\right)12h& =& 240\left(\frac{1}{12}\right)\\ h& =& 20\end{array}$

Tate needs to work 20 hours to have $360.

4. Sara earns $50 for every lawn she mows. She wants to save $750 this summer. Sara has already mowed three lawns. How many more lawns does she need to mow to reach her goal?

m = lawns to mow

$\begin{array}{rcl}50m+3\left(50\right)& =& 750\\ 50m+150& =& 750\\ & & –150 –150\\ \left(\frac{1}{50}\right)50m& =& 600\left(\frac{1}{50}\right)\\ m& =& 12\end{array}$

Sara must mow 12 more lawns to reach her goal.

5. Natalee and her family took a trip to the botanical gardens where she counted 10 butterflies on a single plant. The ratio of Monarch butterflies to Viceroy butterflies was 2 to 3. How many of each type of butterfly were on the plant?
   
   Hint: The ratio of Monarch butterflies to the total number of butterflies is 2 to 5. You can apply the same idea to Viceroy butterflies.

$\begin{array}{rcl}& & m: \mathrm{Monarch}, v: \mathrm{Viceroy}, t: \mathrm{total}\\ & & \\ & & \begin{array}{ccccc}\frac{m}{v}=\frac{2}{3}& & \frac{m}{t}=\frac{2}{5}& or& \frac{v}{t}=\frac{3}{5}\\ & & \frac{m}{10}=\frac{2}{5}& & \frac{v}{10}=\frac{3}{5}\\ & & 5m=\left(2\right)\left(10\right)& & 5v=\left(3\right)\left(10\right)\\ & & 5m=20& & 5v=30\\ & & \left(\frac{1}{5}\right)5m=20\left(\frac{1}{5}\right)& & \left(\frac{1}{5}\right)5v=30\left(\frac{1}{5}\right)\\ & & m=4& & v=6\\ & & 10–4=6& & 10–6=4\end{array}\end{array}$

Natalee saw 4 Monarch butterflies and 6 Viceroy butterflies on the plant.