Proportions are created when we set two ratios equal to each other. They help us convert between rates.
Example:
⇒ In this example, we are solving for x.
⇒ Question example: For every 4 stars, there are 8 hearts. How many hearts will there be for 6 stars?
To solve proportions, we can cross multiply. This means multiplying the numerator of one fraction by the denominator of the other fraction.:
[tex]\dfrac{4\hspace{3}stars}{8\hspace{3}hearts}=\dfrac{6\hspace{3}stars}{x\hspace{3}hearts}\\\\4x=6*8[/tex]
We're given:
Set up a proportion:
[tex]\dfrac{8\hspace{3}minutes}{96\hspace{3}calories}= \dfrac{14\hspace{3}minutes}{x\hspace{3}calories}[/tex]
⇒ Let x be equal to the number of calories the jogger would burn in 14 minutes.
Cross multiply:
[tex]8x=14*96\\8x=1344\\x=168[/tex]
Therefore, the jogger would burn 168 calories in 14 minutes of jogging.
