Problem 1 :
A jar contains 7.5 liters of milk. Lily adds 25.8 grams of sugar and 3.4 liters of water. How much liquid is in the jar?
Solution :
Amount of liquid in the jar :
= 7.5 + 3.4
= 10.9 liters
Problem 2 :
James has $25.65, Charles has $12.75A and Kristen has 19.78. How much money do they all have together?
Solution :
Amount of money that James, Charles and Kristen have together :
= 26.65 + 12.75 + 19.78
= $59.18
Problem 3 :
A bag contains 22.75 cups of sugar. If 2.95 cups of sugar is used for making cookies, find the amount of sugar will be left in the bag.
Solution :
Amount of sugar will be left in the bag after using 2.95 cups of sugar for making cookies :
= 22.75 - 2.95
= 19.8 cups
Problem 4 :
Olivia had $25.55 and Jessica had $23.75. They planned to spend the money together and bought candies for $8.75. How much money did they have after having bought candies?
Solution :
Amount of money that Olivia and Jessica had together after having bought candies :
= 25.55 + 23.75 - 8.75
= 49.30 - 8.75
= $40.55
Problem 5 :
Add the following two decimal numbers with the given conditions.
2.a9 + 3.5b
Conditions :
(i) a + b = 7
(ii) a and b are positive integers and a is an even prime number.
Solution :
It is given that a is an even prime number. We know that 2 is the only even prime number and also it is a positive integer.
a = 2
It is given that a + b = 7.
a + b = 7
2 + b = 7
Subtract 2 from both sides.
b = 5
Since 5 is a positive integer, 5 can be accepted as a value for b.
2.a9 + 3.5b :
= 2.29 + 3.55
= 5.84
Problem 6 :
Evaluate the following expression with the given conditions.
5.7a - 2.b4
Conditions :
(i) a = 3
(ii) b is two times of a.
Solution :
It is given that a = 3 and b is two times of a.
b = 2 ⋅ a
b = 2 ⋅ 3
b = 6
5.7a - 2.b4 :
= 5.73 - 2.64
= 3.09
Problem 7 :
Find the value k in the equation given below.
2.7k + 3.21 = 5.93
Solution :
From the above addition two decimal numbers, it is clear that
k + 1 = 3
Subtract 1 from both sides.
k = 2
Problem 8 :
Find the values of x and y in the equation given below.
3.5x + y.78 = 5.32
Solution :
From the above addition decimal numbers,
x + 8 = 12 or 22 or 32.....
If x + 8 = 22 or 32, x has to be a two-digit number. But, it's not possible. So x + 8 must be equal to 12.
x + 8 = 12 x = 4 |
1 + 3 + y = 5 y + 4 = 5 y = 1 |
Problem 9 :
Find the value of y in the equation given below.
3.74 - 1.3y = 2.38
Solution :
From the initial investigation, we get
4 - y = 9
But, the equation above may be wrong. Because, any positive single digit number y subtracted from 4 will never yield the result 9. And also, the difference between the digits 7 and 3 at tenths place is 3 in the result. Actual difference between 7 and 3 is 4.
From this, we may guess that 1 would have been borrowed from the digit 7 at tenths place to the digit 4 at hundredths place.
Then the above subtraction as follows.
Therefore,
14 - y = 9
Subtract 14 from both sides.
-y = -5
Multiply both sides by -1.
y = 5
Problem 10 :
P, Q and R are three places located on a straight line as shown below.
The distance between the places P and Q is 438.68 miles and that of P and R is 809.95 miles. Find the distance between the places Q and R.
Solution :
Distance between the places Q and R :
QR = PR - PQ
QR = 809.95 - 438.68
QR = 371.27 miles
Problem 11 :
Find the sum of two decimal numbers a.b and b.a, given
a + b = 8
a - b = 3
Solution :
a + b = 8 ----(1)
a - b = 2 ----(2)
(1) + (2) :
2a = 10
a = 5
Substitute a = 5 in (1).
5 + b = 8
b = 3
a.b + b.a :
= 5.3 + 3.5
= 8.8
Problem 12 :
x and y are prime numbers such that
x < 10, y < 10, x > y
If x and y add up to 12, evaluate the following expression.
3.8x - 2.yy
Solution :
Given : x and y add up to 12.
x + y = 12
List out the prime numbers less than 10.
2, 3, 5, 7
Among the above prime numbers less than 10, two numbers satisfy the equation x + y = 12 are 5 and 7.
Since x > y,
x = 7 and y = 5
3.8x - 2.yy :
= 3.87 - 2.55
= 1.32
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