Leon drew AABC and ADEF so that ZA: LD, ZB: LE, AB = 4, and DE = 8.
1 answer:
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Answer:
C. 1000 loss.
Step-by-step explanation:
Let x represent purchase price of each car.
We have been given that a used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car.
We can represent the car that dealer sold with 25% profit to find purchase price as:
Therefore, the purchase price of 1st car was $16,000.
We can represent the car that dealer sold with 20% loss to find purchase price as:
Therefore, the purchase price of 2nd car was $25,000.
The total purchase price of both cars would be
The total sale price of both cars .
We can see that the sale price of both car is less than purchase price by $1000, so the dealer got a loss of $1000.
Therefore, the dealer's total loss, in dollars, for the two transactions combined was 1000 and option C is the correct choice.
Answer:
[a,b] divides n
Step-by-step explanation:
Let us denote the least common multiple of a and b [a,b]=m.
We want to prove that m divides n, where n is a multiple of a and b.
We suppose m does not divide n, then by the Division Theorem, there exists q and r integers such that:
(1) ... n=mq+r, where 0<r<m
As n is a multiple of a and b, there exists s and t integers such that:
sa=n and tb=n
Same thing happens to m as it is the least common multiple, there exists u and v such that:
ua=m and vb=m
So (1) has the following form:
n=mq+r ⇒ sa=uaq+r ⇒sa-uaq=r⇒(s-uq)a=r and
n=mq+r ⇒ tb=vbq+r ⇒ tb-vbq=r⇒ (t-vq)b=r
So r is a multiple of a and b, but r<m which is a contradiction as, m is the least common multiple of a and b. So this concludes the proof.
So this means that is and integer.
As m= vb, then is an integer, lets say
=v; and as m=ua, then
=u.
So v=
=a, so
divides a; on the other hand,
u=
=b, so
divides b. From this we can conclude that
is a common divisor of a and b.