Let's analyze the problem step-by-step:
- Total people = 100
- People who can speak English = 72
- People who can speak French = 43
We need to find how many people speak only English (i.e., speak English but not French). To solve this, we need to find the number of people who speak both English and French first. Let:
- EEE = number of English speakers = 72
- FFF = number of French speakers = 43
- BBB = number of people who speak both English and French
- E_onlyE\_only E_only = number of people who speak only English
We know:
E_only=E−BE\_only =E-BE_only=E−B
Also, the total number of people is 100, so:
People who speak only French=F−B\text{People who speak only French}=F-BPeople who speak only French=F−B
The total number of people can be expressed as:
E_only+(F−B)+B+(people who neither speak English nor French)=100E\_only +(F-B)+B+(\text{people who neither speak English nor French})=100E_only+(F−B)+B+(people who neither speak English nor French)=100
But without information about how many speak neither, we cannot find the exact number unless it is assumed that everyone speaks at least one language. If we assume everyone speaks at least one of the two languages, then:
E_only+(F−B)+B=100E\_only +(F-B)+B=100E_only+(F−B)+B=100
(E−B)+(F−B)+B=100(E-B)+(F-B)+B=100(E−B)+(F−B)+B=100
E+F−B=100E+F-B=100E+F−B=100
B=E+F−100=72+43−100=15B=E+F-100=72+43-100=15B=E+F−100=72+43−100=15
Now,
E_only=E−B=72−15=57E\_only =E-B=72-15=57E_only=E−B=72−15=57
Answer: If everyone speaks at least one language, then 57 people speak only English. If not, then we don't have enough information to determine the exact number.
