Question

the ratio of tomatoes to red apples is 2:5. if there is 20 tomato,hiw many red apple are there

Answer 1

the ratio of tomatoes to red apples is

$\frac{2}{5}$

this ratio must be the same when you have 20 tomatoes, this means that:

$\frac{2}{5}=\frac{20}{x}$

where x is the (unknow) number of apples. Hence, we have:

$\begin{gathered} \frac{2}{5}=\frac{20}{x}\Rightarrow x(\frac{2}{5})=20 \\ \text{hence} \\ x=\frac{20}{\frac{2}{5}} \\ \end{gathered}$

then, we need to divide 20 into 2/5. We can do that by applying the "sandwich law":

$\begin{gathered} x=\frac{20}{\frac{2}{5}}=\frac{\frac{20}{1}}{\frac{2}{5}} \\ x=\frac{20\cdot5}{1\cdot2} \\ x=10\cdot5 \\ x=50 \end{gathered}$

therefore, if there are 20 tomatoes, we have 50 apples.