SOLUTION: 1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28

Question 388187: 1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28 boxes. find the total number of matches ?
2.mr. ong makes regular business trips to kaulalumpur a distance of 420 km from singapore (a)on his way up to kaulalumpur he travels along the trunk road at an average speed of x km/h. write down the expression in trm of x for the time taken in hours to travel from singapore to kaulalumpur
(b)on his return journey to singapore he travels along the north south highway and increases the average speed by 15 km/h.write down the expression in term of x for the time taken in the hours to travel from kaulalumpur to singapore.
(c)if the time difference between the two journey is 40 min from an equation in x and show that it reduces x^2+15x-9540=0
(d)solve the equation and find the time taken for the trip from singapore to kaulalampur
3.mr. kumar lives in the eastern part of the singapore. he visits his aged parents who lives 36 km away, evry weekends. he finds that if he increases the average speed of his vehicle by 12 km/h.he could save 9 min of his travelling time. find the speed at which he travels before the increase in speed.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28 boxes. find the total number of matches ?
:
Let x = no. of matches in each box originally (24 boxes)
then
(x-4) = no. of matches in each box when there is 28 boxes
:
the total no. of matches remain the same, therefore:
28(x-4) = 24x
28x - 112 = 24x
28x - 24x = 112
4x = 112
x = 112/4
x = 18 matches in each box originally
total: 18 * 24 = 432
check it
14 * 28 = 432
:
:
2.mr. ong makes regular business trips to kaulalumpur a distance of 420 km from singapore
(a)on his way up to kaulalumpur he travels along the trunk road at an average speed of x km/h.
write down the expression in trm of x for the time taken in hours to travel from singapore to kaulalumpur
t(x) =
:
(b)on his return journey to singapore he travels along the north south highway
and increases the average speed by 15 km/h.
write down the expression in term of x for the time taken in the hours to travel from kaulalumpur to singapore.
t(x) =
:
(c)if the time difference between the two journey is 40 min from an equation
in x and show that it reduces x^2+15x-9540=0
convert 40 min to 2/3 hrs
- =
Multiply equation by 3x(x+15) to clear the denominators, results:
1260(x+15) - 1260x = 2x(x+15)
1260x + 18900 - 1260x = 2x^2 + 30x
A quadratic equation
2x^2 + 30x - 18900 = 0
Simplify, divide by 2
x^2 + 15x - 9450 = 0; (not 9540 is stated above)
:
:
(d)solve the equation and find the time taken for the trip from singapore to kaulalampur
You can use the quadratic formula, but this equation will factor to:
(x+105)(x-90) = 0
x = 90 km/hr from S to K
:
:
3.mr. kumar lives in the eastern part of the singapore.
he visits his aged parents who lives 36 km away, evry weekends.
he finds that if he increases the average speed of his vehicle by 12 km/h.
he could save 9 min of his travelling time.
find the speed at which he travels before the increase in speed.
:
Let x = his original speed
Convert 9 min to 3/20 hr
- =
Solve this equation exactly like we did above (2.)
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