Question

. Jerusha has two bowls of fruit on her kitchen table. In one bowl she has a ratio of 1 apple to every 2 bananas.In the second bowl she has a ratio of 2 plums to every 3 oranges. Both bowls have the same total number offruit. How many are there of each fruit? (Give one possible assortment.)

Answer 1

Given the following ratios

$\begin{gathered} Ratio\text{ of apple to banana is}\rightarrow1:2 \\ Ratio\text{ of plum to oraange }\rightarrow2:3 \end{gathered}$

By adding the ratios we have that:

$\begin{gathered} 1+2=3\rightarrow case\text{ 1} \\ 2+3=5\rightarrow case\text{ 2} \\ \\ The\text{ LCM of the cases is}\rightarrow3\times5=15 \end{gathered}$

From the L.C.M above, we can deduce that the total number of fruit in each bowl is 15. Thus,

$\begin{gathered} For\text{ }\rightarrow1:2 \\ \frac{1}{3}\times15=\frac{15}{3}=5 \\ \\ \frac{2}{3}\times15=\frac{30}{3}=10 \\ There\text{ are 5 apples and 10 bananas} \end{gathered}$$\begin{gathered} For\rightarrow2:3 \\ \frac{2}{5}\times15=\frac{30}{5}=6 \\ \\ \frac{3}{5}\times15=\frac{45}{5}=9 \\ \\ There\text{ are 6 plums and 9 oranges} \end{gathered}$

Hence, there are 5 apples, 10 bananas, 6 plums, and 9 oranges