A proportion is a statement that two ratios are equal: a:b = c:d, \({a \over b} = {c \over d}\). To solve proportions with a variable term, **cross-multiply**: \({a \over 8} = {3 \over 6} \), 6a = 24, a = 4.

In a class of 23 students, 14 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?

13 | |

7 | |

10 | |

21 |