What's the meaning of Ju in Ju Yi Fan San Zhong

What's the meaning of Ju in Ju Yi Fan San Zhong

To enumerate or illustrate

1. There are 400 grams of salt water with 20% salt content, and how much salt is added to make salt water with 10% salt content? 2. There are 400 grams of sugar water with 20% salt content, and how much water is added to make salt water with 10% salt content?

You have made a mistake in writing the title. The first question should be that the original salt content is 10%, and it becomes 20% after adding salt
According to the meaning of the title, we can know that there is 400 * 10% salt in the raw brine = 40 G
Then the equation: (x + 40) / (400 + x) = 20%, and the solution is x = 50
According to the meaning of the title, it can be known that there is 400 * 20% salt in the raw brine = 80 G
Then the equation: 80 / (400 + x) = 10%, the solution is x = 400

Solving problems of binary linear equations
A says to B: "I think when you are so old, your age is half of my age this year. When you are my age, my age is twice your age this year, 7 less."
A and B solve the system of equations {ax + by = 2, a correctly solves {x = 3, B misinterprets C, and solves {x = - 2,
{cx-7y=8, {y=-2. {y=2,
Find the value of a, B and how much C?
Two questions, thank you

1) Let a's present age be x and Y respectively
x/2 = y-(x-y)；
2y-7= x+(x-y)；
The results of solving the equations are: x = 28, y = 21
So the age of a and B is 28 and 21 respectively
2) The equations are ax + by = 2,
cx-7y=8,
The correct solution of a, x = 3, y = - 2, is given to the above equations
3a-2b=2,----------------①
3C + 14 = 8, C = - 2,
The wrong solution of B is put into the equations
-2a+2b=2,---------------②
-2c-14 = 8, C = - 3,
A = 4, B = 5 can be obtained by solving the new sum equations
So the values of a and B are 4 and 5 respectively, and B takes C as - 3

The exercises of binary linear equations should have answers
For binary linear equations, these two days, to have an answer

1) 66x+17y=3967
25x+y=1200
Answer: x = 48, y = 47
(2) 18x+23y=2303
74x-y=1998
Answer: x = 27, y = 79
(3) 44x+90y=7796
44x+y=3476
Answer: x = 79, y = 48
(4) 76x-66y=4082
30x-y=2940
Answer: x = 98, y = 51
(5) 67x+54y=8546
71x-y=5680
Answer: x = 80, y = 59
(6) 42x-95y=-1410
21x-y=1575
Answer: x = 75, y = 48
(7) 47x-40y=853
34x-y=2006
Answer: x = 59, y = 48
(8) 19x-32y=-1786
75x+y=4950
Answer: x = 66, y = 95
(9) 97x+24y=7202
58x-y=2900
Answer: x = 50, y = 98
(10) 42x+85y=6362
63x-y=1638
Answer: x = 26, y = 62
(11) 85x-92y=-2518
27x-y=486
Answer: x = 18, y = 44
(12) 79x+40y=2419
56x-y=1176
Answer: x = 21, y = 19
(13) 80x-87y=2156
22x-y=880
Answer: x = 40, y = 12
(14) 32x+62y=5134
57x+y=2850
Answer: x = 50, y = 57
(15) 83x-49y=82
59x+y=2183
Answer: x = 37, y = 61
(16) 91x+70y=5845
95x-y=4275
Answer: x = 45, y = 25
(17) 29x+44y=5281
88x-y=3608
Answer: x = 41, y = 93
(18) 25x-95y=-4355
40x-y=2000
Answer: x = 50, y = 59
(19) 54x+68y=3284
78x+y=1404
Answer: x = 18, y = 34
(20) 70x+13y=3520
52x+y=2132
Answer: x = 41, y = 50
(21) 48x-54y=-3186
24x+y=1080
Answer: x = 45, y = 99
(22) 36x+77y=7619
47x-y=799
Answer: x = 17, y = 91
(23) 13x-42y=-2717
31x-y=1333
Answer: x = 43, y = 78
(24) 28x+28y=3332
52x-y=4628
Answer: x = 89, y = 30
(25) 62x-98y=-2564
46x-y=2024
Answer: x = 44, y = 54
(26) 79x-76y=-4388
26x-y=832
Answer: x = 32, y = 91
(27) 63x-40y=-821
42x-y=546
Answer: x = 13, y = 41
(28) 69x-96y=-1209
42x+y=3822
Answer: x = 91, y = 78
(29) 85x+67y=7338
11x+y=308
Answer: x = 28, y = 74
(30) 78x+74y=12928
14x+y=1218
Answer: x = 87, y = 83
(31) 39x+42y=5331
59x-y=5841
Answer: x = 99, y = 35
(32) 29x+18y=1916
58x+y=2320
Answer: x = 40, y = 42
(33) 40x+31y=6043
45x-y=3555
Answer: x = 79, y = 93
(34) 47x+50y=8598
45x+y=3780
Answer: x = 84, y = 93
(35) 45x-30y=-1455
29x-y=725
Answer: x = 25, y = 86
(36) 11x-43y=-1361
47x+y=799
Answer: x = 17, y = 36
(37) 33x+59y=3254
94x+y=1034
Answer: x = 11, y = 49
(38) 89x-74y=-2735
68x+y=1020
Answer: x = 15, y = 55
(39) 94x+71y=7517
78x+y=3822
Answer: x = 49, y = 41
(40) 28x-62y=-4934
46x+y=552
Answer: x = 12, y = 85
(41) 75x+43y=8472
17x-y=1394
Answer: x = 82, y = 54
(42) 41x-38y=-1180
29x+y=1450
Answer: x = 50, y = 85
(43) 22x-59y=824
63x+y=4725
Answer: x = 75, y = 14
(44) 95x-56y=-401
90x+y=1530
Answer: x = 17, y = 36
(45) 93x-52y=-852
29x+y=464
Answer: x = 16, y = 45
(46) 93x+12y=8823
54x+y=4914
Answer: x = 91, y = 30
(47) 21x-63y=84
20x+y=1880
Answer: x = 94, y = 30
(48) 48x+93y=9756
38x-y=950
Answer: x = 25, y = 92
(49) 99x-67y=4011
75x-y=5475
Answer: x = 73, y = 48
(50) 83x+64y=9291
90x-y=3690
Answer: x = 41, y = 92
(51) 17x+62y=3216
75x-y=7350
Answer: x = 98, y = 25
(52) 77x+67y=2739
14x-y=364
Answer: x = 26, y = 11
(53) 20x-68y=-4596
14x-y=924
Answer: x = 66, y = 87
(54) 23x+87y=4110
83x-y=5727
Answer: x = 69, y = 29
(55) 22x-38y=804
86x+y=6708
Answer: x = 78, y = 24
(56) 20x-45y=-3520
56x+y=728
Answer: x = 13, y = 84
(57) 46x+37y=7085
61x-y=4636
Answer: x = 76, y = 97
(58) 17x+61y=4088
71x+y=5609
Answer: x = 79, y = 45
(59) 51x-61y=-1907
89x-y=2314
Answer: x = 26, y = 53
(60) 69x-98y=-2404
21x+y=1386
Answer: x = 66, y = 71
(61) 15x-41y=754
74x-y=6956
Answer: x = 94, y = 16
(62) 78x-55y=656
89x+y=5518
Answer: x = 62, y = 76
(63) 29x+21y=1633
31x-y=713
Answer: x = 23, y = 46
(64) 58x-28y=2724
35x+y=3080
Answer: x = 88, y = 85
(65) 28x-63y=-2254
88x-y=2024
Answer: x = 23, y = 46
(66) 43x+50y=7064
85x+y=8330
Answer: x = 98, y = 57
(67) 58x-77y=1170
38x-y=2280
Answer: x = 60, y = 30
(68) 92x+83y=11586
43x+y=3010
Answer: x = 70, y = 62
(69) 99x+82y=6055
52x-y=1716
Answer: x = 33, y = 34
(70) 15x+26y=1729
94x+y=8554
Answer: x = 91, y = 14
(71) 64x+32y=3552
56x-y=2296
Answer: x = 41, y = 29
(72) 94x+66y=10524
84x-y=7812
Answer: x = 93, y = 27
(73) 65x-79y=-5815
89x+y=2314
Answer: x = 26, y = 95
(74) 96x+54y=6216
63x-y=1953
Answer: x = 31, y = 60
(75) 60x-44y=-352
33x-y=1452
Answer: x = 44, y = 68
(76) 79x-45y=510
14x-y=840
Answer: x = 60, y = 94
(77) 29x-35y=-218
59x-y=4897
Answer: x = 83, y = 75
(78) 33x-24y=1905
30x+y=2670
Answer: x = 89, y = 43
(79) 61x+94y=11800
93x+y=5952
Answer: x = 64, y = 84
(80) 61x+90y=5001
48x+y=2448
Answer: x = 51, y = 21
(81) 93x-19y=2
86x-y=1548
Answer: x = 18, y = 88
(82) 19x-96y=-5910
30x-y=2340
Answer: x = 78, y = 77
(83) 80x+74y=8088
96x-y=8640
Answer: x = 90, y = 12
(84) 53x-94y=1946
45x+y=2610
Answer: x = 58, y = 12
(85) 93x+12y=9117
28x-y=2492
Answer: x = 89, y = 70
(86) 66x-71y=-1673
99x-y=7821
Answer: x = 79, y = 97
(87) 43x-52y=-1742
76x+y=1976
Answer: x = 26, y = 55
(88) 70x+35y=8295
40x+y=2920
Answer: x = 73, y = 91
(89) 43x+82y=4757
11x+y=231
Answer: x = 21, y = 47
(90) 12x-19y=236
95x-y=7885
Answer: x = 83, y = 40
(91) 51x+99y=8031
71x-y=2911
Answer: x = 41, y = 60
(92) 37x+74y=4403
69x-y=6003
Answer: x = 87, y = 16
(93) 46x+34y=4820
71x-y=5183
Answer: x = 73, y = 43
(94) 47x+98y=5861
55x-y=4565
Answer: x = 83, y = 20
(95) 30x-17y=239
28x+y=1064
Answer: x = 38, y = 53
(96) 55x-12y=4112
79x-y=7268
Answer: x = 92, y = 79
(97) 27x-24y=-450
67x-y=3886
Answer: x = 58, y = 84
(98) 97x+23y=8119
14x+y=966
Answer: x = 69, y = 62
(99) 84x+53y=11275
70x+y=6790
Answer: x = 97, y = 59
(100) 51x-97y=297
19x-y=1520
Answer: x = 80, y = 39
That's enough

Binary linear equations
It is known that the solutions of the equations ax + by = 3, BX + ay = 7 about X and y are x = 2, y = 1. Find the value of a + B
THANKS!

The solution of AX + by = 3, BX + ay = 7 is x = 2, y = 1
So it's true to take x = 2, y = 1 into the original equation, so
2a+b=3
2b+a=7
Two formula addition
3a+3b=10
a+b=10/3

The problem is solved by a system of linear equations of two variables
1. Port a and port B are 80 km apart. A ship starts from port a and sails upstream for 5 hours to port B, while sails downstream from port B for 4 hours to Port A. It is known that the speed of the ship sailing downstream and upstream is the sum and difference of the ship's speed in still water and water flow speed, and the speed and water flow speed of the ship in still water are calculated
2. When someone went to Baique temple from TIANTI, because he was worried, he went up three steps at a time. As a result, there was only one step left at the top of the mountain, so he had to go up another step. When he came back, he went down two steps at a time, just to the bottom of the mountain. He counted it. How many steps did he go up? How many steps did he have?
3. During May Day, a school organizes students of Grade 7 and grade 8 to go on an outing to a scenic spot. The ticket price of the scenic spot is 15 yuan per person. If 50-99 students can buy tickets at 20% discount, and more than 100 students can buy tickets at 60% discount. It is known that there are less than 50 students of Grade 7 and more than 50 students of Grade 8, but less than 100 students, If you buy discount tickets together, you should pay 1080 yuan
(1) Is the total number of students in Grade 7 and 8 participating in the outing more than 100
(2) How many students are there in Grade 7 and grade 8?

1. Let the ship speed be x in still water and Y in water, then the ship speed is x + y in downstream and X-Y in upstream
5(X-Y)=80
4(x+y)=80
x=18,y=2
2. There are x steps up the mountain and Y steps on the steps
3x+1=y
2(x+160）=y
X=319,Y=958
3. There are x and y people in 7 and 8 years old respectively
1. Assume that the total number of people aged 7 and 8 does not exceed 100
15x+15X0.8y=1575
15X0.8X（x+y）=1080
X = 165. It does not meet the conditions, so the total number of people aged 7 and 8 is more than 100
2.15x+15X0.8y=1575
15X0.6X(x+y)=1080
x=45,y=75
Don't forget to add points

Solving problems of binary linear equations
What is the value of / M-N / when the solution of the system of equations 3x-y = m of X is x = 1?
x+my=n y=1

The solution is x = m + Y / 3
Then M + Y / 3 = 1
M+Y=3
Because y = 1
Then M = 2
X+MY=N
N=3
Then / M-N / = - 1

Exercises of binary linear equations
120 questions

1.2x+9y=81
3x+y=34
2.9x+4y=35
8x+3y=30
3.7x+2y=52
7x+4y=62
4.4x+6y=54
9x+2y=87
5.2x+y=7
2x+5y=19
6.x+2y=21
3x+5y=56
7.5x+7y=52
5x+2y=22
8.5x+5y=65
7x+7y=203
9.8x+4y=56
x+4y=21
10.5x+7y=41
5x+8y=44
11.7x+5y=54
3x+4y=38
12.x+8y=15
4x+y=29
13.3x+6y=24
9x+5y=46
14.9x+2y=62
4x+3y=36
15.9x+4y=46
7x+4y=42
16.9x+7y=135
4x+y=41
17.3x+8y=51
x+6y=27
18.9x+3y=99
4x+7y=95
19.9x+2y=38
3x+6y=18
20.5x+5y=45
7x+9y=69
21.8x+2y=28
7x+8y=62
22.x+6y=14
3x+3y=27
23.7x+4y=67
2x+8y=26
24.5x+4y=52
7x+6y=74
25.7x+y=9
4x+6y=16
26.6x+6y=48
6x+3y=42
27.8x+2y=16
7x+y=11
28.4x+9y=77
8x+6y=94
29.6x+8y=68
7x+6y=66
30.2x+2y=22
7x+2y=47
1) 66x+17y=3967
25x+y=1200
Answer: x = 48, y = 47
(2) 18x+23y=2303
74x-y=1998
Answer: x = 27, y = 79
(3) 44x+90y=7796
44x+y=3476
Answer: x = 79, y = 48
(4) 76x-66y=4082
30x-y=2940
Answer: x = 98, y = 51
(5) 67x+54y=8546
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