２題英文Form2數

The sum of the two digits of a two-digit number is 9.
If the digits are reversed, the number will be increased by 45.
Find the original number.
let the number is xy
then the reverse number is yx
we have
x+y=9...(1)
10x+y+45=10y+x
9x+45=9y
x+5=y...(2)
from 1
x=9-y
sub into 2
9-y+5=y
y=7
x=9-7=2
the original number is 27
Mr Chan buys a total of 80kg of lemon candies and mango candies.
The prices of the lemon candies and mango candies are $40 per kg and $50 per kg
respectively. He mixes these candies and sells them for $70 per kg,
making a profit of 60%
let the ratio of lemon candies and mango candies is x:1-x
then
the cost of the mixed candies
=40x+50(1-x)
=50-10x per kg
we get
[70-(50-10x )]/(50-10x )=60%
10x+20=30-6x
16x=10
x=10/16=0.625
so the ratio of lemon candies and mango candies is 0.675:0.375
he buys total of 80kg of lemon candies and mango candies
So, lemon candies have
80*0.675=50kg
and mango candies have
30kg
total cost
=40*50+50*30
=200+150
=350