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Question 29808: Good evening,please could you help me to solve these problems
Find the value of X so that the line passing through (x,1) and (3,-x)has slope 5.
Another one about the "Age" Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how is Ben now in terms of P?
Please!!!!!! help me. your faithfully student (Modi21)
Found 2 solutions by stanbon, sdmmadam@yahoo.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! slope= (-x-1)/(3-x)=5
(x+1)=-5(3-x)
x+1=-15+5x
4x=16
x=4
Age Problem:
"6-yr ago data":
Let Ben be "x" yrs. old
Then Anita was Px yrs old
"current-yr data":
Anita is now Px+6=17 yrs old
Ben is now x+6 yrs old
Now, express Ben's age in terms of P.
Using Px+6=17 you get
x=11/P
Therefore Ben = x+6= [(11/P)+6] yrs. old
Cheers,
Stan H.
Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website! Find the value of X so that the line passing through (x,1) and (3,-x)
has slope 5.
The slope of the line joining two given points P(x1,y1) and Q(x2,y2) is given by
m = (y2-y1)/(x2-x1) ----(1)
And here P(x1,y1) = (x,1) and Q(x2,y2) = (3,-x)
Therefor x1 = x,y1=1; x2 = 3 and y2 = -x
Slope of the line joining the given points is 5
That is given that m=5
Therefore applying (1)
5 = [(-x)-(1)]/[(3)-(x)]
5=(-x-1)/(3-x)
Multiplying by (3-x)
5(3-x) = -x-1
15-5x = -x-1
15+1 = -x+5x
16 = 4x
That is 4x = 16
x = 16/4 = 4
Answer:x = 4
Verification: The given points are now P(4,1) and Q(3,-4) (using x = 4)
By definition slope = [(-4)-1]/(3-4) (using (1)
= (-5)/(-1) = 5 which is correct
Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how is Ben now in terms of P?
Let Anitha be A years old and
let Ben be B years old
six years ago
Anitha was (A-6) yrs old and Ben was (B-6) yrs old
At that time Anitha was P times as old as Ben was
That is (A-6) = P(B-6)----(1)
And Anitha is now 17 yrs old.
That is A = 17 ----(2)
Putting A = 17 in (1)
(17-6)= PB-6P
11= PB - 6P
11+6P = PB
That is PB = (11+6P)
Therefore B = (11+6P)/P (dividing by P)
Verification:Put B = (11+6P)/P in (1)
RHS = P(B-6)
=P[(11+6P)/P-6]
=P[11+6P-6P}/P
=11
=(17-6)
=A-6 (as A= 17)
=LHS
Therefore our value is correct
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