Problem 1 :
A cup contains 112.35 ml of hot milk. Olivia adds 5 grams of coffee powder and 25.76 ml of hot water into the cup. How much liquid is in the cup?
Problem 2 :
A box with chemical powder weighs 2.45. If the empty box weighs 0.26 lbs., find the weight of the chemical powder.
Problem 3 :
For a treatment Mr. James took 2.63 grams of a medicine on Monday, 3.12 grams of the same medicine on Wednesday and 2.48 grams on Friday of the same week. How much medicine did Mr. James take altogether in the week?
Problem 4 :
Sophia had $32.56. She bought candies for $5.28 and gave $17.49 to her friend. How much money has Sophia left?
Problem 5 :
Add the following two decimal numbers with the given conditions.
3.x7 + 5.4y
Conditions :
(i) x + y = 5
(ii) Both x and y are prime numbers and y is an even number.
Problem 6 :
The sum of two decimal numbers is 58.456. If one of the numbers is 48.9, find the other number.
Problem 7 :
The value of (A - B) is 25.36. If the value of B is 4.723, find the value of A.
Problem 8 :
X and Y are two decimal numbers such that
X - Y = 7.8
If X = 7.84, find the value of Y.
Problem 9 :
Evaluate the following expression with the given conditions.
m.63 - 3.n4
Conditions :
(i) n = 8.
(ii) m is one-half of n.
Problem 10 :
Find the value of (x.yx + y.yyx), given
x + y = 9
x – y = 1
Problem 11 :
Three cities named P, Q and R are located on a straight line as shown below.
The distance between the cities P and Q is 798.45 miles and that of Q and R is 350.86 miles. Find the distance between the cities P and Q.
Problem 12 :
The decimal number 2.7x is increased by 3.21 and the resulting number is 5.93. Find the value of x.
Problem 13 :
3.5x more than y.78 is equal to 5.32. Find the value of x.
Problem 14 :
1.3y less than 3.74 is equal to 2.38. Find the value of y.
1. Answer :
Amount of liquid in the cup :
= 112.35 + 25.76
= 138.11 liters
2. Answer :
Weight of the chemical powder :
= 2.45 - 0.26
= 2.19 lbs.
3. Answer :
Amount of medicine that Mr. James took altogether in the week :
= 2.63 + 3.12 + 2.48
= 8.23 grams
4. Answer :
Amount of money that Sophia has left :
= 32.56 - 5.28 - 17.49
= 27.28 - 17.49
= $9.79
5. Answer :
Given : x + y = 5 and both x and y are prime numbers and y is an even number.
Then,
x = 3 and y = 2
3.x7 + 5.4y
= 3.37 + 5.42
= 8.79
6. Answer :
Given : The sum of two decimal numbers is 58.456 and one of the them is 48.9.
The other decimal number :
= 58.456 - 48.9
= 9.556
7. Answer :
Given : A - B = 25.36 and B = 4.723.
A - B = 25.36
A - 4.723 = 25.36
Add 4.723 to both sides.
A = 25.36 + 4.723
A = 30.083
8. Answer :
X - Y = 7.8
Substitute X = 7.84.
7.84 - Y = 7.8
Subtract 7.84 from both sides.
-Y = -0.04
Multiply both sides by -1.
Y = 0.04
9. Answer :
It is given that n = 8 and m is one-half of n.
m = ½ ⋅ n
Substitute n = 8.
m = ½ ⋅ 8
m = 4
m.63 - 3.n4 :
= 4.63 - 3.84
= 0.79
10. Answer :
x + y = 9 ----(1)
x – y = 1 ----(2)
(1) + (2) :
2x = 10
x = 5
Substitute x = 5 in (1).
5 + y = 9
y = 4
x.yx + y.yyx :
= 5.45 + 4.445
= 9.895
11. Answer :
Distance between the cities P and Q :
PQ = PR - QR
PQ = 798.45 - 350.86
PQ = 447.59 miles
12. Answer :
2.7x + 3.21 = 5.93
In the above addition two decimal numbers 2.7x and 3.21, it is clear that
k + 1 = 3
Subtract 1 from both sides.
k = 2
13. Answer :
3.5x + y.78 = 5.32
In the above addition two decimal numbers 3.5x and y.78,
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) has to be equal to 12.
x + 8 = 12 x = 4 |
1 + 3 + y = 5 y + 4 = 5 y = 1 |
14. Answer :
3.74 - 1.3y = 2.38
From the initial investigation, we get
4 - y = 9
The above equation is wrong. Because, when a positive single digit number y subtracted from 4, the result can not be 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 can 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
-y = -5
y = 5
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