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two word problems

 
1)A car company charges $31 per day to rent a particular type of car and $0.16 per mile. Juan is charged $47.96 for a one day rental. How many mile did he drive?
a)121mi
b)106mi
c)300mi
d)269mi
 
2) The number if mosquitos M(x), in millions, in a certain area depends on the june rain fall x, in inches, according to the function M(x)=18.0x-x^2, what rainfall produces the maximum number of mosquitoes? round the answer to the nearest tenth.
a)9.0in
b)18.0in
c)324.0n
d)0.0in
 
 

Comments

if i did my math right i believe the first one is b and the second one is a 
am i right ?
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4 Answers

I'm not the greatest with math but the first one is simple enough!
 
47.96 (total charged)
31 (base rate for 1 day rental)
 
47.96 - 31 = 16.96
 
16.96 / .16 = 106 ; therefore, Juan drove 106 miles. The Answer is B.
---------------------------------------------------------------------------------------
For the second question....
 
M(x) is mosquitos, in millions
 
x is rainfall in inches.
 
So from here, it's just plug-and-play:
----------------------------------------------------
A) M(x) = 18.0 x (9.0) - 9.0^2 [squared]
M(x) = 162 - 81
 
First option is... M(x)=81
----------------------------------------------------
B) M(x) = 18.0 x (18.0) - 18.0^2 [squared]
M(x) = 324 - 324 = 0
Second option is... M(x) = 0
----------------------------------------------------
C) M(x) = 18.0 x (324.0) - 324.0^2 [squared]
M(x) = 5,832 - 104,976 = -99,144
Third option is... M(x)= -99,144
----------------------------------------------------
D) M(x) = 18.0 x (0.0) - 0.0^2 [squared]
M(x) = 0 - 0 = 0
Last option is... M(x) = 0
 
If I've worked through this second equation correctly the answer to the second problem will be A

Comments

Theresa you are more than welcome! If you need any further assistance with reading/writing/research papers, etc. (Anything that would fall in the English subjects of study) feel free to reach out to me!
 
Best Regards,
 
Dominic J. :D
For question 1, we translate english directly into math:  Cost = $31 + $0.16*miles or C = .16m + 31.  We are given the total cost C, so we can directly solve for m.
 
For question 2, the most direct way is to differentiate the equation with respect to x and set it equal to zero:
 
dM/dx = 18 -2x.  Setting equal to zero we get -2x+18 = 0 yielding x = 9 for the best amount of rainfall for mosquitoes.  We can be sure this is a true global maximum by the fact that the equation is a quadratic concave downward.
$47.96-$31.00=$16.96
$16.96/$0.16=1696/16=106 miles, b)
 
M(x)=18x-x^2
M(x)=x(18-x)
x>0 and x<18
0<x<18
x is between 0 and 18, not including 0 and not including 18
that eliminates b,c, and d
a) 9 in is between 0 and 18
1) 31+ 0.16m=47.96
.16m=16.96
 
m=106 miles b)
 
2) y=18x-x^2 is a parabola that opens down with a maximum at its vertex.
 
The x coordinate of the vertex is -b/2a where a b c are the coefficients of the polynomial y=ax^2+bx+c
In our case a=-1 b=18 c=0
so xv=-b/2a=-18/-2=9 
 
A rainfall of 9 inches produces the maximum.. which can be found out by plugging in 9 for x in the initial equation.
 
For extra help, look up youtube videos on finding maximums and minimums of quadratic functions/parabolas.