CBSE Class 7 Mathematics Simple Equations Worksheet Set 02

Question 1(a). Write the following statements in the form of equations: The sum of four times y and 14 is 42.
Answer: Four times y is written as \(4y\). The sum of \(4y\) and 14 is \(4y + 14\).
Therefore, the equation is \(4y + 14 = 42\).
In simple words: Translate the words directly into mathematical operations to form the equation.
Exam Tip: Keywords like "sum of" mean addition (+), "times" means multiplication (\(\times\)), and "is" means equals (=).

Question 1(b). Write the following statements in the form of equations: If you subtract 7 from 5 times a number is 28.
Answer: Let the number be \(x\). Five times the number is \(5x\). Subtracting 7 from \(5x\) gives \(5x - 7\).
Therefore, the equation is \(5x - 7 = 28\).
In simple words: First write five times the number as \(5x\), then subtract 7 from it and equate it to 28.

Exam Tip: "Subtract 7 from 5 times a number" means \(5x - 7\), not \(7 - 5x\).

Question 1(c). Write the following statements in the form of equations: one fourth of m is 4 more than 9
Answer: One fourth of \(m\) is written as \(\frac{m}{4}\). "4 more than 9" is written as \(9 + 4\) or \(13\).
Therefore, the equation is \(\frac{m}{4} = 9 + 4\) or \(\frac{m}{4} = 13\).
In simple words: Divide \(m\) by 4 and set it equal to 9 plus 4.

Exam Tip: "More than" indicates addition to the base number.

Question 1(d). Write the following statements in the form of equations: one third of a number plus 8 is 29.
Answer: Let the number be \(x\). One third of the number is \(\frac{x}{3}\). Adding 8 gives \(\frac{x}{3} + 8\).
Therefore, the equation is \(\frac{x}{3} + 8 = 29\).
In simple words: Take one third of a variable, add 8, and equate to 29.

Exam Tip: Fractions of a number like "one third of x" should always be written as \(\frac{x}{3}\) or \(\frac{1}{3}x\).

Question 2(a). Solve the equation: \(x - 2 = 0\)
Answer: Given equation: \(x - 2 = 0\)
Transposing \(-2\) to the right side:
\(x = 0 + 2\)
\(x = 2\)
In simple words: Move \(-2\) across the equals sign and change its sign to \(+2\).

Exam Tip: Whenever you transpose a term from one side to the other, its sign reverses (+ becomes -, and - becomes +).

Question 2(b). Solve the equation: \(y + 8 = -8\)
Answer: Given equation: \(y + 8 = -8\)
Transposing \(8\) to the right side:
\(y = -8 - 8\)
\(y = -16\)
In simple words: Move \(+8\) to the right side to get \(-8 - 8\), which equals \(-16\).

Exam Tip: Be careful with negative integers: \(-8 - 8\) results in \(-16\), not \(0\).

Question 2(c). Solve the equation: \(4m = 16\)
Answer: Given equation: \(4m = 16\)
Dividing both sides by 4:
\(m = \frac{16}{4}\)
\(m = 4\)
In simple words: Since 4 is multiplied by \(m\), divide 16 by 4 to find the value of \(m\).

Question 2(d). Solve the equation: \(\frac{x}{4} = 12\)
Answer: Given equation: \(\frac{x}{4} = 12\)
Multiplying both sides by 4:
\(x = 12 \times 4\)
\(x = 48\)
In simple words: Multiply 12 by 4 to find the value of \(x\).

Exam Tip: Division in an equation is undone by multiplication on both sides.

Question 2(e). Solve the equation: \(\frac{y}{8} = \frac{9}{13}\)
Answer: Given equation: \(\frac{y}{8} = \frac{9}{13}\)
Multiplying both sides by 8:
\(y = \frac{9 \times 8}{13}\)
\(y = \frac{72}{13}\)
In simple words: Multiply both sides by 8 to isolate \(y\).

Exam Tip: When multiplying a fraction by a whole number, multiply the whole number with the numerator.

Question 3. When one-third of a number is added to 5 we get 8. Find the number.
Answer: Let the required number be \(x\).
According to the question:
\(\frac{x}{3} + 5 = 8\)
Transposing 5 to the right side:
\(\frac{x}{3} = 8 - 5\)
\(\frac{x}{3} = 3\)
Multiplying both sides by 3:
\(x = 3 \times 3\)
\(x = 9\)
In simple words: Set up the equation, subtract 5 from 8, and then multiply the result by 3 to get the number 9.

Exam Tip: Always verify your answer by substituting it back into the statement: one-third of 9 is 3, and 3 + 5 = 8.

Question 4. When we multiply a number by 6 and subtract 5 from its product, we get 7. Find the number.
Answer: Let the required number be \(x\).
According to the question:
\(6x - 5 = 7\)
Transposing \(-5\) to the right side:
\(6x = 7 + 5\)
\(6x = 12\)
Dividing both sides by 6:
\(x = \frac{12}{6}\)
\(x = 2\)
In simple words: Form the equation \(6x - 5 = 7\), add 5 to 7 to get 12, and divide by 6 to find \(x = 2\).

Exam Tip: Solve two-step equations by first eliminating addition/subtraction, then multiplication/division.

Question 5. When five is added to a number we get 35. Find the number.
Answer: Let the required number be \(x\).
According to the question:
\(x + 5 = 35\)
Transposing 5 to the right side:
\(x = 35 - 5\)
\(x = 30\)
In simple words: Subtract 5 from 35 to find the number, which is 30.

Exam Tip: Simple linear equations can often be solved in a single transposition step.

Question 6. Thrice a number when decreased by one fourth gives 11. Find the number.
Answer: Let the required number be \(x\).
Thrice the number is \(3x\).
According to the question:
\(3x - \frac{1}{4} = 11\)
Transposing \(-\frac{1}{4}\) to the right side:
\(3x = 11 + \frac{1}{4}\)
\(3x = \frac{44}{4} + \frac{1}{4}\)
\(3x = \frac{45}{4}\)
Dividing both sides by 3:
\(x = \frac{45}{4 \times 3}\)
\(x = \frac{15}{4}\)
In simple words: Form the equation \(3x - \frac{1}{4} = 11\), add \(\frac{1}{4}\) to 11, and divide by 3 to find the fraction \(\frac{15}{4}\).

Exam Tip: When adding a fraction to a whole number, take the common denominator to simplify calculation.

Question. If two complementary angles differ by 20°, find the measure of each angles.
Answer : 35°, 55°

Question. Find 3 odd consecutive numbers whose sum is 27.
Answer : 7, 9, 11.

Question. 6z + 10 = – 2x
Answer : z = –2

Question. Find the multiple of 8, if the sum of two consecutive multiples of 8 is 184.
Answer : 88, 96.

Question. Twice a number when decreased by 7 gives, 15 find the number.
Answer : x = 11

Question. The sum of present ages of Sameer and his father is 54 years. 6 years ago, his father was 6 times as old as his son. Find their present ages.
Answer : 12 years, 42 years

Question. The age of Nishant and Sanjay are in the ratio 4 : 5. Ten years hence the ratio of their ages will be 6 : 7. Find their present ages.
Answer : 20 years and 25 years

Question. The angles of a triangle are (3x)°; (2x + 60)° and (5x – 40)°. Find each angle.
Answer : 48°, 92°, 40°

Question. A number is 2/5 times another number. If their sum is 70, find the numbers.
Answer : 20, 50

Question. 2.8y = 54 + y.
Answer : y = 30

Question. After 12 years. Manoj will be 3 times as old as he was 4 yrs. ago. What is his present age?
Answer : 12 years.

Question. 5x + 0.7 = 2.9
Answer : x = 0.44

Question. 3x – 5 = 0. 5.
Answer : x = 5/3

Question. What is the number which when multiplied by 20 gives the product 120?
Answer : 6

Question. If x = y – 2 and x/y – x+1/y = 1, find x and y.
Answer : y = –1; x = –3.

Question. 0.16 (5x – 2) = 0.4 (x + 1).
Answer : x = 1.8

Question. Two supplementary angles differ by 40°. Find their measure.
Answer : 70°, 110°

Question. A number is as much greater than 21 as it is less than 71. Find the number.
Answer : 46

Question. 7P+8/9 = 9
Answer : P = 73/7

Question. 5x + 3 = 4/3 (1+x)
Answer : x = –5/11

Question. If 2 is subtracted from a number, then tripled, the result is 4 more than the given number. Find the number.
Answer : 5

Question. Find a number which when multiplied by 5 is increased by 80.
Answer : 20

Question. If x = y – 3, find the value of y from the equation y – x-y/3 = 4/5 (y-x)
Answer : y = 7/5

Question. The numerator of a rational number is 7 less than the denominator. If the denominator is increased by 9 and the numerator is also increased by 2, we again get the same rational number. Determine the number.
Answer : 2/9

Question. Find the measure of an angle, if its supplement measures 39° more than twice its complement.
Answer : 39°

Question. A number when added to its half gives 72. Find the number.
Answer : 48