# 9.2.1. Ratio

The ratio between two integer numbers is . If 3 is added to the first number and 7 is subtracted from the second number, the ratio between them becomes . Determine the two numbers.

• A,
• B6, 12
• C,
• D62, 124
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If a certain number is added to the two terms of the ratio , the ratio becomes . Find that number.

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If the square of a certain number is added to each of the two terms of the ratio , the ratio becomes . Find the number.

• A 17
• B 5
• C 25
• D 10
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If we subtract thrice a certain number from each of the two terms of the ratio , the ratio becomes . Find the number.

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If , and 24 are proportional, determine the value of .

• A
• B 288
• C
• D 289
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If , find .

• A
• B
• C
• D3
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If , and are proportional, .

• A
• B
• C
• D
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If , and 19 are proportional, find .

• A 95
• B
• C
• D
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If , determine .

• A
• B
• C
• D
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Determine the ratio between the areas of two squares; the first has a side length of , and the second has a side length of .

• A
• B
• C
• D
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A sum of money is distributed between two people with a ratio of . If the share of the first is LE, then the share of the other is .

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If , where and , find .

• A
• B
• C
• D
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If , find , where .

• A
• B
• C
• D
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If , find .

• A
• B
• C 460
• D
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If , determine where both and .

• A
• B
• C
• D
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If , determine .

• A
• B
• C
• D
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If , find .

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If and , determine the ratio of .

• A
• B
• C
• D
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If , determine .

• A
• B
• C
• D
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If , find .

• A
• B
• C
• D
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If , determine .

• A
• B
• C
• D26
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Given that the perimeter of a rectangle equals cm, and the ratio between the lengths of two of its sides is , determine its area.

• A
• B
• C
• D
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Determine the two positive real numbers whose ratio is , and the square of the small number exceeds 7 times the great number by 560.

• A196, 256
• B80, 70
• C28, 32
• D
3 920
,
4 480
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The success rate of the third preparatory in a governorate is , where the percentage of success of the boys is , and that of the girls is . Determine the ratio between the number of boys and the number of girls in this grade.

• A
• B
• C
• D
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The ratio between the base length and the height of a triangle is , and its area is . Find the lengths of the base and the height.

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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Find the positive number whose multiplicative inverse can be added to the consequent of the ratio so it becomes .

• A3
• B10
• C13
• D4
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Determine the four proportional numbers of which the fourth proportional equals the square of the second, the first is less than the second by 1, and the third is 72.

• A or
• B or
• C or
• D or
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If , , , and are four proportional numbers, where , , and , find , , , and .

• A, , ,
• B, , ,
• C, , ,
• D, , ,
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Find the third proportional to 3, 33, and 11.

• A 363
• B 121
• C 33
• D 1
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Find the number that should be added to each of the numbers 39, 32, 30, and 24 to make them proportional.

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If , find .

• A or
• B or
• C or
• D or
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If , find in its simplest form.

• A
• B
• C
• D
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If , find the ratio .

• A
• B
• C
• D
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The ratio between two integer numbers is . If 33 is subtracted from each number, the ratio between them becomes . Determine the two numbers.

• A 4 and 10
• B 6 and 1
• C 6 and 15
• D 1 and 15
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Find the middle proportional between 16 and 4.

• A 10 and
• B 64 and
• C 8 and
• D 20 and
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