數學題一問<急>! .........

1. Susan, Katie and Flora buy a birthday gift for $500 together. If K
atie contributed 2 times as much as Susan, and Flora spends $50 less t
han Katie, find the amount contributed by Susan.
Let S$ be the amount contributed by Susan.
500=Katie's contribution+Susan's contribution+Flora's contribution
=2S+S+(2S-50)
=5S-50
550=5S
S=110


2. Stephanie and Dennis go hiking together. They go uphill at a spee
d of 3km/h and downhill at a speed of 4km/h. If the lengths of the uph
ill and the downhill paths are the same, and Stephanie and Dennis spe
nd a total of 4.2 hours in completing their journey, find the total lengt
h of the journey.
Let Lkm be length of uphill path and downhill path.
Total time= uphill time + downhill time
=uphill length/uphill speed + downhill time/downhill speed
4.2hr=(L/3km+L/4km)hr
4.2=7L/12
7.2=L
Total length of journey=uphill length + downhill length
=2Lkm
=14.4km
3. In a two-digit number, the units digit is greater than the tens digit
by 3. If the tens digit and the units digit of the number are interchange
d, the sum of the number obtained and the original number is 121. Fin
d the two numbers.
Let t be tens digit and u be units digit, then
u=t+3
Value of the original number = 10t+u
Value of the number formed by interchanging the digits= 10u+t
Sum of the two numbers=10t+u+10u+t=121
11u+11t=121
u+t=11
As u=t+3, u+t=t+3+t=11
2t+3=11
t=4
u=t+3=7
Therefore the two numbers are 47 and 74.