COME!HELP!!! (方程)There have two questions

2006-11-15 6:03 am
Complete to answer me.............
1)Mr.Chan is putting some oranges into some boxes.If each box contains 50 oranges,he needs one more box.If each box contains 55 oranges,one box is left.How many boxes and oranges are there?
2)The sum of the digits of a two-digit number is 7.If 2 is added to each digit ,then the new number will be 3 less than twice the original numbe.Find this two-digit number.

回答 (3)

2006-11-15 6:36 am
✔ 最佳答案
1)Mr. Chan is putting some oranges into some boxes. If each box contains 50 oranges, he needs one more box. If each box contains 55 oranges, one box is left. How many boxes and oranges are there?
assume he have x oranges,
such that
x/55 + 1 = x/50 – 1
2 = x/50 – x/55
1100 = 11x – 10x
x = 1100
and he has x/55 + 1 = 1100/55 + 1 = 21 boxes
He has 21 boxes and 1100 oranges

2) The sum of the digits of a two-digit number is 7. If 2 is added to each digit, then the new number will be 3 less than twice the original number. Find this two-digit number.
assume the digit ten is x
such that this number equal to 10x + (7 – x)
according to this question
10(x+2) + (7-x+2) = 2[10x + (7 – x)] – 3
10x+20 + 7-x + 2 = 20x + 14 – 2x – 3
9x + 29 = 18x + 11
18 = 9x
x = 2
so that this number is 25
2006-11-15 6:50 am
1. Let a be the no. of oranges & y be the no. of boxs

a / (y+1) = 50 --- (1)
a / (y-1) = 55 --- (2)

In(1),
a / (y+1) = 50
a = 50( y+1 )

In(2),
a / (y-1) = 55
a = 55( y-1 )

Combine a = 50( y+1 ) & a = 55( y-1 ), that is

50( y+1 ) = 55( y-1 )
50y + 50 = 55y - 55
5y = 105
y = 21

Put y = 21 into a = 55( y-1 )

a = 55( 21-1 )
a = 55 x 20
a = 1100

Hence, the no. of oranges is 1100 & the no. of boxs is 21.

2. Let a be the digit of the number & b be the tenth digit of the number

a + b = 7 --- (1)
(a + 2) + 10(b + 2) = (a + 10b) - 3 --- (2)

In (1),
a + b= 7
a = 7 - b

Put a = 7 - b into (2)
(a + 2) + (10b + 2) = (a + 10b) - 3
(7 - b + 2) + 10(b + 2) = 2(7 - b + 10b) - 3
9 - b + 10b + 20 = 14 + 18b - 3
29 + 9b = 11 + 18b
9b = 18
b = 2

Put b = 2 into (1)
a + 2 = 7
a = 5

Hence, the two-digit number is 25.
2006-11-15 6:26 am
help到你第一條,唔明你第二條問咩= =
let there are x oranges and y boxs
x/50=y+1
x/55=y-1

x/50-x/55=2
x/550=2
x=1100
y=21

if there is ok ,plx tell me what's the second question asking...
參考: myself


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