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# Number Theory/Algebra Solution

Question
Hello:

Can the answer to the following be determined by using algebra?  If so, what would be the solution?

4 carpenters can build 8 houses in 10 days.  2 carpenters can build how many houses in 15 days?

Hello Kenneth

I don't think we need algebra.  In the given information, 8 houses were built with 40 carpenter days of work.  So each house takes 5 carpenter days. In the problem we have 30 carpenter days, so 6 can be built.
However we can use the idea of joint proportionality.  The number of houses built is jointly proportioal to the number of carpenters and the number of days.  So h = kcd where k is a constant.  Substituting the given: 8 = k*40, so k = 1/5.  Our formula is then h = cd/5.
Best wishes
vijilant
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and explanation!

Number Theory

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#### Vijilant

##### Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

##### Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 £50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.