Introduction to solving proportions:
If two fractions` x/y` and `p/q` are equal, they are said to be in proportion. It can be denoted by x: y :: p: q.
Here the fractions should be of same kind and same unit. The two quantities in a ratio are called its terms. The first term is called antecedent and the second term is called consequent. A ratio is a pure numbers it has no unit.
In the proportion x: y :: p: q, x and q are called extremes, and y and p are called means
Example Problems on Solving Proportions:
Ex 1. A bottle machine fills 500 bottles in 15 minutes. How many bottles will it fill in `1 1/2` hours?
Sol: Let x be the number of bottles to be filled in `1 1/2` hours = 90 minutes.
Given: `x / 90` = `500 / 15`
`=>` x = `500 xx 90 / 15`
x = 3000 bottles.
Therefore 3000 bottles can be filled in 90 minutes.
Ex 2: A machine prints four books in 10 minutes. How many will it print is 2 hours?
Sol : Let ‘x’ be the number of books need to be printed in 2 hours = 120 minutes.
Given: `x / 120` = `4 / 10`
`=>` x = `4 xx120 / 10` = 48
Therefore 48 books can be printed in 2 hours.
Ex 3: Find the value of x, if 7 : 18 : : x : 27
Sol : Given: 7 : 18 : : x : 27
`=>` ` 7 / 18 = x / 27`
`=>` `18 xx x = 7 xx 27`
Therefore x = `7 xx 27 / 18` = `21 / 2` = 10.5
Ex 4: If x is the mean proportion of 2 and 32, find x?
Sol : Given: 2 : x : : x : 32
`=>` `2/ x = x / 32 `
`=>`` x ^2 = 2 xx 32`
Therefore x 2 = 64
Therefore x = 8.
Ex 5: Find the third proportional to 2 and 32.
Soln: Let x be the third proportional :
We have 2 : 32 = 32 : x
`=>` `2 / 32 = 32 / x`
`=>` 2 x = 32 2
`=>` x =` 32 ^2 / 2` = 512.
I like to share this Ordering Whole Numbers with you all through my article.
Practice Problems on Solving Proportions.
If 5 pen costs 8 dollar, what is the cost of 15 pens?
[Ans: 15 pens = 24 dollar]
2. Find the value of x in the proportion 4 : x : : 12 : 9
[Ans : x = 3 ]
3. Find the value of x in 5 : 7 : : 8 : x
[Ans: x = 11.2]
If two fractions` x/y` and `p/q` are equal, they are said to be in proportion. It can be denoted by x: y :: p: q.
Here the fractions should be of same kind and same unit. The two quantities in a ratio are called its terms. The first term is called antecedent and the second term is called consequent. A ratio is a pure numbers it has no unit.
In the proportion x: y :: p: q, x and q are called extremes, and y and p are called means
Example Problems on Solving Proportions:
Ex 1. A bottle machine fills 500 bottles in 15 minutes. How many bottles will it fill in `1 1/2` hours?
Sol: Let x be the number of bottles to be filled in `1 1/2` hours = 90 minutes.
Given: `x / 90` = `500 / 15`
`=>` x = `500 xx 90 / 15`
x = 3000 bottles.
Therefore 3000 bottles can be filled in 90 minutes.
Ex 2: A machine prints four books in 10 minutes. How many will it print is 2 hours?
Sol : Let ‘x’ be the number of books need to be printed in 2 hours = 120 minutes.
Given: `x / 120` = `4 / 10`
`=>` x = `4 xx120 / 10` = 48
Therefore 48 books can be printed in 2 hours.
Ex 3: Find the value of x, if 7 : 18 : : x : 27
Sol : Given: 7 : 18 : : x : 27
`=>` ` 7 / 18 = x / 27`
`=>` `18 xx x = 7 xx 27`
Therefore x = `7 xx 27 / 18` = `21 / 2` = 10.5
Ex 4: If x is the mean proportion of 2 and 32, find x?
Sol : Given: 2 : x : : x : 32
`=>` `2/ x = x / 32 `
`=>`` x ^2 = 2 xx 32`
Therefore x 2 = 64
Therefore x = 8.
Ex 5: Find the third proportional to 2 and 32.
Soln: Let x be the third proportional :
We have 2 : 32 = 32 : x
`=>` `2 / 32 = 32 / x`
`=>` 2 x = 32 2
`=>` x =` 32 ^2 / 2` = 512.
I like to share this Ordering Whole Numbers with you all through my article.
Practice Problems on Solving Proportions.
If 5 pen costs 8 dollar, what is the cost of 15 pens?
[Ans: 15 pens = 24 dollar]
2. Find the value of x in the proportion 4 : x : : 12 : 9
[Ans : x = 3 ]
3. Find the value of x in 5 : 7 : : 8 : x
[Ans: x = 11.2]
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