Somma, differenza e rapporto tra numeri. Completi di soluzione guidata. Arithmetic

Somma, differenza e rapporto tra numeri. Completi di soluzione guidata.

Arithmetic – Ratio, sum and difference of numbers (Proportion)

1. _{x:y=3:22 con x+ y=75 soluzione}

2. 𝑥: 𝑦 = 3: 4 con 𝑥 + 𝑦 = 70 ^soluzione

3. 𝑥: 𝑦 = 2: 7 con 𝑥 + 𝑦 = 45 ^soluzione

4. 𝑥: 𝑦 = 5: 3 con 𝑥 − 𝑦 = 20 ^soluzione

5. 𝑥: 𝑦 = 2: 3 con 𝑥 + 𝑦 = 20 ^soluzione

6. _{x:y=19:6 con x+y=75 soluzione}

7. 𝑥: 𝑦 = 7: 3 con 𝑥 − 𝑦 = 16 8. _{x:y=12:7 con x−y =10} 9. _{x:y=7:4 con x− y=33} 10. _{x:y=17:8 con x− y=45} 11. _{x:y=12:7 con x−y =10} 12. _{x:y=35:16 con x−y=38} 13. _{x:y=4:3 con x+ y=21} 14. _{x:y=13:9 con x− y=36} 15. _{x:y=13:9 con x−y=8}

16. 𝑥: 𝑦 = 2: 5 𝑐𝑜𝑛 𝑥 + 𝑦 = 28 17. 𝑥: 𝑦 = 7: 4 𝑐𝑜𝑛 𝑥 − 𝑦 = 36

18. 𝑥: 5 = 𝑦: 7 = 𝑧: 2 𝑐𝑜𝑛 𝑥 + 𝑦 + 𝑧 = 42 19. 𝑥: 3 = 𝑦: 6 = 𝑧: 15 𝑐𝑜𝑛 𝑥 + 𝑦 + 𝑧 = 16 20.

7 11 :18 4

:y=15 con x−y= x

21. 𝑥: 𝑦 =4 5:2

3 𝑐𝑜𝑛 𝑥 + 𝑦 =3 4 22. 𝑥: 𝑦 =5

2:4

3 𝑐𝑜𝑛 𝑥 − 𝑦 =6 5

23. _{x:y=24:9 con x}²_{+ y}² ₌₇₃ 24. _{x:y=22:14 con x}² _+y² ₌₁₇₀ 25. 𝑥: 𝑦 = 15: 6 𝑐𝑜𝑛 𝑥²+ 𝑦² = 29 26. 𝑥: 𝑦 = 12: 27 𝑐𝑜𝑛 𝑥²+ 𝑦² = 97

27. _{x:y=60:9 con xy=60} 28. _{x:y=95:15 con xy=57}

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Soluzioni

𝑥 ∶ 𝑦 = 3 ∶ 22 𝑐 𝑜𝑛 𝑥 + 𝑦 = 75 (𝑥 + 𝑦): 𝑥 = (3 + 22): 3

75: 𝑥 = 25: 3 𝑥 =75 ⋅ 3

25 = 3 ⋅ 3 = 9

𝑦 = (𝑥 + 𝑦) − 𝑥 = 75 − 9 = 66

EQUAZIONI

𝑥 ∶ 𝑦 = 3 ∶ 22 𝑐 𝑜𝑛 𝑥 + 𝑦 = 75 𝑥 + 𝑦 = 75 → 𝑥 = 75 − 𝑦

75 − 𝑦

𝑦 = 3

22 75 − 𝑦

𝑦 ∙ 𝑦= 3 22∙ 𝑦 75 − 𝑦+ 𝑦= 3

22𝑦+ 𝑦 75 = 25

22𝑦 →25

22𝑦 = 75 25

22𝑦∙22

25= 75∙22 25 𝑦 = 66

𝑥 = 75 − 66 = 9

𝑥 ∶ 𝑦 = 3 ∶ 4 con 𝑥 + 𝑦 = 70 (𝑥 + 𝑦): 𝑥 = (3 + 4): 3

70: 𝑥 = 7: 3 𝑥 =70 ∙ 3

7 = 10 ∙ 3 = 30

𝑦 = (𝑥 + 𝑦) − 𝑥 = 70 − 30 = 40

EQUAZIONI

𝑥 ∶ 𝑦 = 3 ∶ 4 con 𝑥 + 𝑦 = 70 𝑥 + 𝑦 = 70 → 𝑥 = 70 − 𝑦 70 − 𝑦

𝑦 = 3

4 70 − 𝑦

𝑦 ∙ 𝑦= 3 4∙ 𝑦 70 − 𝑦+ 𝑦= 3

4𝑦+ 𝑦 70 = 7

4𝑦 →7

4𝑦 = 70 7

4𝑦∙4

7= 70∙4 7 𝑦 = 40

𝑥 = 70 − 40 = 30

𝑥: 𝑦 = 2: 7 con 𝑥 + 𝑦 = 45 (𝑥 + 𝑦): 𝑥 = (2 + 7): 2

45: 𝑥 = 9: 2 𝑥 =45 ∙ 2

9 = 5 ∙ 2 = 10

𝑦 = (𝑥 + 𝑦) − 𝑥 = 45 − 10 = 35

𝑥: 𝑦 = 5: 3 con 𝑥 − 𝑦 = 20 (𝑥 − 𝑦): 𝑥 = (5 − 3): 5

20: 𝑥 = 2: 5 𝑥 =20 ∙ 5

2 = 10 ∙ 5 = 50

𝑦 = 𝑥 − (𝑥 − 𝑦) = 50 − 20 = 30

𝑥: 𝑦 = 2: 3 con 𝑥 + 𝑦 = 20 (𝑥 + 𝑦): 𝑥 = (2 + 3): 2

20: 𝑥 = 5: 2 𝑥 =20 ∙ 2

5 = 4 ∙ 2 = 8

𝑦 = (𝑥 + 𝑦) − 𝑥 = 20 − 8 = 12

( )

6 25 3

6 75

6 : 25 : 75

6 : ) 6 19 ( : ) (

75 6

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𝑥: 𝑦 = 7: 3 con 𝑥 − 𝑦 = 16 (𝑥 − 𝑦): 𝑥 = (7 − 3): 7

16: 𝑥 = 4: 7 𝑥 =16 ∙ 7

4 = 4 ∙ 7 = 28

𝑦 = 𝑥 − (𝑥 − 𝑦) = 28 − 16 = 12

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24 12 5 2

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70 35 19 2

35 38

35 : 19 : 38

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12 4 7 3

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𝑥: 𝑦 = 13: 9 𝑐𝑜𝑛 𝑥 − 𝑦 = 36 (𝑥 − 𝑦): 𝑥 = (13 − 9): 13

36: 𝑥 = 4: 13 𝑥 =36 · 13

4 = 9 · 13 = 117 𝑦 = 117 − 36 = 81

𝑥: 𝑦 = 13: 9 𝑐𝑜𝑛 𝑥 − 𝑦 = 8 (𝑥 − 𝑦): 𝑥 = (13 − 9): 13

8: 𝑥 = 4: 13 𝑥 =8 · 13

4 = 2 · 13 = 26 𝑦 = 26 − 8 = 18

𝑥: 𝑦 = 2: 5 𝑐𝑜𝑛 𝑥 + 𝑦 = 28 (𝑥 + 𝑦): 𝑥 = (2 + 5): 2

28: 𝑥 = 7: 2 𝑥 =28 · 2

7 = 4 · 2 = 8

𝑦 = (𝑥 + 𝑦) − 𝑥 = 28 − 8 = 20

𝑥: 𝑦 = 7: 4 𝑐𝑜𝑛 𝑥 − 𝑦 = 36 (𝑥 − 𝑦): 𝑥 = (7 − 4): 7

36: 𝑥 = 3: 7 𝑥 =36 · 7

3 = 12 · 7 = 84 𝑦 = 84 − 36 = 48

x : 5 = y : 7 = z : 2 con x + y + z = 42 (x+y+z):x = (5+7+2):5

42:x=14:5

x = 42  5 : 14 = 15

(x+y+z):y = (5+7+2):7 42:y=14:7

y=42  7 : 14 = 21

z = 42 - (21 + 15) = 42 - 36 = 6

x : 3 = y : 6 = z : 15 con x + y + z = 16 (x+y+z):x=(3+6+15):3

16:x=24:3

x = 16  3 : 24 = 2

(x+y+z):y=(3+6+15):6 16:y=24:6

y= 16  6 : 24 = 4

z = 16 - (2 + 4) = 16 - 6 = 10

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24 11 35 11

1 35 7 1 5 3 7 1 1 15 33 28 4 11 15

4 :15 28 : 33 11

4 :15 28

72 : 105

11

4 :15 7 18 4 : 15

7 11 :18 4 : 15

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𝑥 ∶ 𝑦 =4 5∶ 2

3 𝑐𝑜𝑛 𝑥 + 𝑦 =3 4 (𝑥 + 𝑦): 𝑥 = (4

5+2 3) :4

5 3

4: 𝑥 = (12 + 10 15 ) :4

5 3

4: 𝑥 =22 15:4

5 𝑥 =3

4∙4 5∙15

22=3 1∙ 3

22= 9 22 𝑦 = (𝑥 + 𝑦) − 𝑥 =3

4− 9

22=33 − 18 44 = 15

44

𝑥: 𝑦 =5 2:4

3 𝑐𝑜𝑛 𝑥 − 𝑦 =6 5 (𝑥 + 𝑦): 𝑥 = (5

2−4 3) :5

2 6

6: 𝑥 = (15 − 8 6 ) :5

2 6

5: 𝑥 =7 6:5

2 𝑥 =6

5∙5 2∙6

7=3 1∙6

7=18 7 𝑦 = 𝑥 − (𝑥 − 𝑦) − 𝑥 = 18

7 −6

5= 90 − 42 35 =48

35

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3 9 8

64

9 64 73 7 64

5 6

576 3 7

576 : 657 :

73

576 : ) 81 576 ( : ) (

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11 121 7

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𝑥: 𝑦 = 15: 6 𝑐𝑜𝑛 𝑥²+ 𝑦² = 29 𝑥²: 𝑦² = 15²: 6²

(𝑥² + 𝑦²): 𝑥² = (225 + 36): 225 29: 𝑥² = 261: 225

𝑥² = 29 ∙ 225

261 =225 9 = 25

𝑥 = √25 = 5 𝑦 = √(𝑥² + 𝑦²) − 𝑥² = √29 − 25 = √4 = 2

𝑥: 𝑦 = 12: 27 𝑐𝑜𝑛 𝑥²+ 𝑦² = 97 𝑥²: 𝑦² = 12²: 27²

(𝑥² + 𝑦²): 𝑥² = (144 + 729): 144 97: 𝑥² = 873: 144

𝑥² = 97 ∙ 144

873 =144 9 = 16

𝑥 = √16 = 4 𝑦 = √(𝑥² + 𝑦²) − 𝑥² = √97 − 16 = √81 = 9

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20 400

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19 3 57 57

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Keywords

Matematica, Aritmetica, Proporzionalità, Proporzioni, calcolo del termine

incognito di una proporzione, estremi, medi, proporzioni, risolvere una proporzione, Somma, differenza e rapporto tra numeri, ricerca termine incognito, incognita, x, medio proporzionale, esercizi con soluzioni

Math, Arithmetic, Proportion, Proportionality, proportion properties, extremes, means, solving a proportion, proportionality problem, Ratio sum and difference of numbers, Ratio, Math solved exercises

Matemática, Aritmética, Proporción Mathématique, Arithmétique, Proportion

Mathematik, Arithmetik, das Verhältnis Arabic: دَدَع ،مْجَح ،هَّيِمَك

Chinese 比例 Czech: poměr Danish: forhold

Dutch: verhouding Estonian: (õige) vahekord

Finnish: suhde Greek: αναλογία Hungarian: arány

Icelandic: hlutfall Indonesian: perbandingan

Japanese: 割合

Korean: (양·크기·수 따위의) 비, 비율 Latvian: proporcija; attiecība; samērs Lithuanian: proporcija, santykis

Norwegian: forhold Polish: proporcja Portuguese: proporção

Romanian: proporţie Russian: пропорция

Slovak: pomer, podiel Slovenian: razmerje

Swedish: proportion Turkish: oran, nisbet