1. ## algebra equations

Hi

I need help on these problems, these are practice problems for my final because the questions will be similar to these but I need help with these.
I am lost.

Any help would be greatly appreciated

1) find average speed if you drive 100 miles half the trip at 60mph nd half
30mph?

and then
Driving 30 minutes @ 45mph and 30 minutes @15mph

2) of a collection of mango fruits the king took 1/6 the queen 1/5 of the
raineder the three chief princes 1/4,1/3 and 1/2 of the successive remainders
and the youngest child took the reamaining 3 mangoes o you who are clever in
miscellaneous problems on fractions give out the measure of the collection of
mangoes???

3) I NEED TO SOLVE THIS PROBLEM BACKWARD BUT I DONT KNOW
i began the day feeling very rich as i was walking to school i met a friend who
had loaned me money and thought this would be a great opportunity to pay her
back so i gave her $15 theni remembered i nedd to buy some school supplies and that took one third of the money in my pocket then i met another friend and she asked me for a loan so i gave her three fourths of the money in my pocket now i had only$10.00 in my pocket how much money didi i start with??

ANY HELP WOULD BE GREATLY APPRECIATED, THANKS IN ADVANCE

2. Originally Posted by miramontes
1) find average speed if you drive 100 miles half the trip at 60mph nd half
30mph?

and then
Driving 30 minutes @ 45mph and 30 minutes @15mph
$\displaystyle v_1=60$
$\displaystyle \frac{s_1}{t_1}=60$
$\displaystyle \frac{50}{t_1}=60$
$\displaystyle t_1=\frac{5}{6}$

$\displaystyle v_2=30$
$\displaystyle \frac{s_2}{t_2}=30$
$\displaystyle \frac{50}{t_2}=30$
$\displaystyle t_2=\frac{5}{3}$

$\displaystyle t=\frac{5}{6}+\frac{5}{3}=2.5$

$\displaystyle v=\frac{s}{t}=\frac{100}{2.5}=40$mph

and then
Driving 30 minutes @ 45mph and 30 minutes @15mph
this means???

Originally Posted by miramontes
2) of a collection of mango fruits the king took 1/6 the queen 1/5 of the
raineder the three chief princes 1/4,1/3 and 1/2 of the successive remainders
and the youngest child took the reamaining 3 mangoes o you who are clever in
miscellaneous problems on fractions give out the measure of the collection of
mangoes???
Let, number of mangoes is $\displaystyle x$.

1st,
King takes $\displaystyle \frac{1}{6}$
Remains $\displaystyle \frac{5}{6}$

2nd,
Queen takes $\displaystyle \frac{1}{5}$
Remains $\displaystyle \frac{4}{5}$

3rd,
The 3 chief princes take $\displaystyle \frac{1}{4}$,$\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{2}$ of the successive remainders
Remain,
$\displaystyle \frac{1}{2}(\frac{2}{3})(\frac{3}{4})(\frac{4}{5}) (\frac{5}{6}x)$

Last,
The youngest child took the reamaining 3 mangoes
Therefore,
$\displaystyle \frac{1}{2}(\frac{2}{3})(\frac{3}{4})(\frac{4}{5}) (\frac{5}{6}x)=3$
$\displaystyle \frac{1}{6}x=3$
$\displaystyle x=18$

Originally Posted by miramontes
3) I NEED TO SOLVE THIS PROBLEM BACKWARD BUT I DONT KNOW
i began the day feeling very rich as i was walking to school i met a friend who
had loaned me money and thought this would be a great opportunity to pay her
back so i gave her $15 theni remembered i nedd to buy some school supplies and that took one third of the money in my pocket then i met another friend and she asked me for a loan so i gave her three fourths of the money in my pocket now i had only$10.00 in my pocket how much money didi i start with??
Let, your money is $\displaystyle x$.

1st,
You remain $\displaystyle x-15$

2nd,
You used $\displaystyle \frac{1}{3}$
therefore, you remain $\displaystyle \frac{2}{3}$
$\displaystyle \frac{2}{3}(x-15)$

Last,
You used $\displaystyle \frac{3}{4}$
Therefore, you remain $\displaystyle \frac{1}{4}$
$\displaystyle \frac{1}{4}[\frac{2}{3}(x-15)]$

$\displaystyle \frac{1}{4}[\frac{2}{3}(x-15)]=10$
$\displaystyle x-15=60$
$\displaystyle x=75$

3. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
thank you so much for your help, I really appreciate it

and then
Driving 30 minutes @ 45mph and 30 minutes @15mph
this means???

this means apply driving 100 miles to the question above.

4. Originally Posted by miramontes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
thank you so much for your help, I really appreciate it

and then
Driving 30 minutes @ 45mph and 30 minutes @15mph
this means???

this means apply driving 100 miles to the question above.
You mean,
1) find average speed if you drive 100 miles 30 minutes @ 45mph and 30 minutes @15mph?

If your mean is like that, I can't solve......

Because,

If driving with speed 45mph for 0.5 hour,
the distance travelled is 0.5(45)miles.

If driving with speed 15mph for 0.5 hour,
the distance travelled is 0.5(15)miles.

Therefore,

The total distance travelled is 30miles.
I am not finish the 100miles distance.