Introduction to word problems in rates and ratios:
Math word problems we solve the problems by replacing the data’s given in the problem by alphabets (text manner) rather than using numerical notation to get the solution of the problem. We can solve the mathematical problems in two steps:
1) Prepare equations with the help of data’s given in the problem.
2) Solve the equations which you have prepared.
Here are some example word problems in rates and ratios:
1) Prepare equations with the help of data’s given in the problem.
2) Solve the equations which you have prepared.
Here are some example word problems in rates and ratios:
Example Word Problems in Rates:
In rates we see problems in related to money and work.
Example 1 [rates]:
Last month Craig earned $330 by working in a shoe company as part time job for 30 hours. Find
a) Find his rate of pay
b) Find how much he would have earned if he had worked for 40 hours.
Given data:
Craig earned by working: $310,
Craig worked for: 30 [hours].
Solution:
a) To find his rate of pay we use:
Rate of pay=money earned/hours worked
=`330/30`
=11 [per hour]
b)To find the earnings if he had worked 40 hours:
= rate xx hours he would work
=`11 xx 40`
=440 [dollars]
Therefore, Craig would have eabrown $440 if he had worked for 40 hours.
Example 2 [rates]:
Two students can wash the car 6 cars in 1 hour. How much would 8 students if they are charged $10 to wash a car?
Given data:
Number of cars two students can wash in an hour: 6 [cars],
Washing one car is charged about: $10.
Solution:
Step 1:
Number of cars which can be washed by 8 students let it be x,
Therefore,
`2/8` =`6/x`
2x=`8 xx 6` ,
2x=48,
x=24.
Step 2:
Total money earned if they charged $10 a car:
=`24 xx 10`
=240 [dollars]
Therefore, they earn $240 by washing cars.
Example 1 [rates]:
Last month Craig earned $330 by working in a shoe company as part time job for 30 hours. Find
a) Find his rate of pay
b) Find how much he would have earned if he had worked for 40 hours.
Given data:
Craig earned by working: $310,
Craig worked for: 30 [hours].
Solution:
a) To find his rate of pay we use:
Rate of pay=money earned/hours worked
=`330/30`
=11 [per hour]
b)To find the earnings if he had worked 40 hours:
= rate xx hours he would work
=`11 xx 40`
=440 [dollars]
Therefore, Craig would have eabrown $440 if he had worked for 40 hours.
Example 2 [rates]:
Two students can wash the car 6 cars in 1 hour. How much would 8 students if they are charged $10 to wash a car?
Given data:
Number of cars two students can wash in an hour: 6 [cars],
Washing one car is charged about: $10.
Solution:
Step 1:
Number of cars which can be washed by 8 students let it be x,
Therefore,
`2/8` =`6/x`
2x=`8 xx 6` ,
2x=48,
x=24.
Step 2:
Total money earned if they charged $10 a car:
=`24 xx 10`
=240 [dollars]
Therefore, they earn $240 by washing cars.
Example Problems in Ratios:
Example 3 [ratios]:
Fred and George have pens at the ratio 6:1.fred gave half of his pens to George. Find the ratio of pen’s that fred and George have at the end.
Solution:
In the question it’s given that Fred has given half of his pens to George.
Therefore, the unit in which Fred has right now,
=62
=3 [units]
Now, George gets 3 units of pens,
Therefore, the unit that George has now=1+3
=4 [units]
Now, the ratio of pens that Fred and George have now is 3:4.
Example 4 [ratios]:
Ricky arranges some brown and green covered book in his self. The ratio of the number of brown covered book to the number green covered books is 2:1.He arranges 9 more green covered books in his self and the ratio becomes 4:5.
Now find the following questions
a) How many Brown covered book are in the box?
b) How many green covered books does Ricky have in the end?
Solution:
The ratio of the number of brown covered books to the number of green covered book is 2:1
Therefore, b=2g ----------- (1)
Now she adds 12 more green books in the shelf and the ratio becomes 4:5
Therefore,
5b=4(g+9)
5b=4g+36 ----- (2)
Now substituting 1 in 2,
We get,
5(2g) =4g+36
10g=4g+36
[Now by moving 4r to the other side, as it is positive sign it becomes negative when placed in the other side.]
10g-4g=36
6g=36
[Now by moving 6 on the other side]
g=`36/6`
g=6.
a) To find the no of brown covered books in the box, we use equation 1:
b=2g
b=2×6 [where b=6]
b=12 [books]
Therefore, the no of brown covered books that Ricky has arranged is 12 books.
b) To find the no of green covered books that Ricky has to arrange at the end, we use the equation,
g=b+12
g=12+12 [where b=12]
g=24.
Therefore, the number of green covered books does Ricky at the end is 24 books
Fred and George have pens at the ratio 6:1.fred gave half of his pens to George. Find the ratio of pen’s that fred and George have at the end.
Solution:
In the question it’s given that Fred has given half of his pens to George.
Therefore, the unit in which Fred has right now,
=62
=3 [units]
Now, George gets 3 units of pens,
Therefore, the unit that George has now=1+3
=4 [units]
Now, the ratio of pens that Fred and George have now is 3:4.
Example 4 [ratios]:
Ricky arranges some brown and green covered book in his self. The ratio of the number of brown covered book to the number green covered books is 2:1.He arranges 9 more green covered books in his self and the ratio becomes 4:5.
Now find the following questions
a) How many Brown covered book are in the box?
b) How many green covered books does Ricky have in the end?
Solution:
The ratio of the number of brown covered books to the number of green covered book is 2:1
Therefore, b=2g ----------- (1)
Now she adds 12 more green books in the shelf and the ratio becomes 4:5
Therefore,
5b=4(g+9)
5b=4g+36 ----- (2)
Now substituting 1 in 2,
We get,
5(2g) =4g+36
10g=4g+36
[Now by moving 4r to the other side, as it is positive sign it becomes negative when placed in the other side.]
10g-4g=36
6g=36
[Now by moving 6 on the other side]
g=`36/6`
g=6.
a) To find the no of brown covered books in the box, we use equation 1:
b=2g
b=2×6 [where b=6]
b=12 [books]
Therefore, the no of brown covered books that Ricky has arranged is 12 books.
b) To find the no of green covered books that Ricky has to arrange at the end, we use the equation,
g=b+12
g=12+12 [where b=12]
g=24.
Therefore, the number of green covered books does Ricky at the end is 24 books
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