Cambridge Math's Milestone Class 6th - ( Page no 116, 117 )

  Cambridge Math's Milestone Class 6th

By Prem Sir Math Solutions 9470710586

Page no 116, 117

Multiple Choice Questions:

1. A symbol which takes on various numerical values is called a/an:

   • Answer: b. variable

2. A statement of equality in which one or two variables are involved is called a/an:

   • Answer: a. equation

3. The value of a variable in an equation is:

   • Answer: b. not fixed

4. Which of the following is not an equation?

   • Answer: d. $3p + 2 < 7$

5. $\frac{2}{3} = 4$ denotes a/an:

   • Answer: c. algebraic equation

6. Which method is used for finding a solution by guessing various values for variables?

   • Answer: b. Trial and error method

7. What is the solution of the equation $x + 1 = 0$?

   • Answer: a. $-1$

8. Find the value of $q$ in the equation $q - 9 = 60$:

   • Answer: d. 69

9. Which of the following is represented by $4s - 3$?

   • Answer: b. 3 subtracted from the product of 4 and $s$

10. Which of the following equations has 0 as the solution?

    • Answer: c. $z + 0 = 0$

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Subjective Questions:

1. The age of Anuja’s father is twice that of her age. After 20 years, her age will be the same as her father’s present age. Find their ages:

   • Let Anuja's age be $x$. Then her father’s age is $2x$.
   • After 20 years: $x + 20 = 2x$.
   • Solving: $2x - x = 20$, $x = 20$.
   • Anuja’s present age: $20$ years.
   • Her father’s age: $2 \times 20 = 40$ years.

2. Johnny had a pile of sheets on his table. He used 7 sheets for his homework and 28 sheets were left unused.

   • Equation: $x - 7 = 28$.
   • Solution: $x = 28 + 7 = 35$.
   • Total sheets: 35.

3. Check by substitution whether the given values of $x$ are the solutions of the equations:

   • $x - 3 = 6; x = 13$: Substitute $x = 13$: $13 - 3 = 10$ (Not a solution).
   • $2x + (7) = 4; x = -5$: Substitute $x = -5$: $2(-5) + 7 = -10 + 7 = -3$ (Not a solution).
   • $2x - 9 = 7; x = 7$: Substitute $x = 7$: $2(7) - 9 = 14 - 9 = 5$ (Not a solution).

4. Fill in the boxes:

   • $\frac{p+1}{4} = 6 \Rightarrow p + 1 = 24 \Rightarrow p = 23$.
     • Answer: $p = 23$.
   • $z + \frac{9}{7} = \frac{9}{7} \Rightarrow z = 0$.
     • Answer: $z = 0$.
   • $5(8 + q) = 45 \Rightarrow 8 + q = 9 \Rightarrow q = 1$.
     • Answer: $q = 1$.

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5. What is $x$ in $2x + 6 = x + 5$?

• Solve: $2x + 6 = x + 5$
• $2x - x = 5 - 6$
• $x = -1$
• Answer: $x = -1$

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6. The variable $z$ stands for a particular number in the equation $2z + 2 = 3z + 4$. What number does $z$ stand for?

• Solve: $2z + 2 = 3z + 4$
• $2z - 3z = 4 - 2$
• $-z = 2$
• $z = -2$
• Answer: $z = -2$

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7. Pick out the solution from the values given in brackets next to each equation:

a. $r + 14 = 25$

• $r = 25 - 14 = 11$
• Solution: $(11, 14, 25)$
• Answer: a. $(11, 14, 25)$

b. $t - 10 = 0$

• $t = 10$
• Solution: $(10, -10, 0)$
• Answer: $(10, -10, 0)$

c. $y + 5 = 4$

• $y = 4 - 5 = -1$
• Solution: $(-1, 0, 1)$
• Answer: c. $(-1, 0, 1)$

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8. Form two equations using the variable $w$ and 10 with the answer being 30.

• Equation 1: $3w = 30$
• Equation 2: $w + 20 = 30$
• Answer:
  1. $3w = 30$
  2. $w + 20 = 30$

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9. Complete the table by trial and error method and find the solution to the equation $x + 13 = 18$:

• Solve: $x + 13 = 18$
• $x = 18 - 13 = 5$
• Fill the table:

$x$	1	2	3	4	5	6	-2	-3
$x + 13$	14	15	16	17	18	19	11	10

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10. A school canteen has two varieties of sandwiches: mixed vegetable sandwich and mushroom sandwich.

• Scenario: On a special day, the number of mushroom sandwiches sold was six more than twice the sale of mixed vegetable sandwiches. Also, there were 40 mushroom sandwiches.
• Let the number of mixed vegetable sandwiches sold = $x$.
• Number of mushroom sandwiches = $2x + 6$.
• Given: $2x + 6 = 40$
• Solve:
  • $2x = 40 - 6$
  • $2x = 34$
  • $x = 17$
• Mixed vegetable sandwiches sold = $17$.

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11. Olivia and Sophia together found 78 seashells on the beach. Olivia found 6 shells.

• Write the equation: $x + 6 = 78$.
• Solve: $x = 78 - 6 = 72$.
• Sophia found 72 shells.

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12. Think of a situation where an algebraic equation is used.

• Example: A farmer grows 3 types of crops. If the total yield of crops is 200 kg, and two crops yield 120 kg, the third crop's yield can be represented by $x + 120 = 200$, where $x$ is the unknown yield.

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13. Create a real-life problem based on the equation $500n + 1500 = 5000$:

• Example: "A gym membership costs $500 per month. An additional one-time joining fee of $1500 is charged. If the total expense is $5000, find the number of months $n$ for which the membership was taken."

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14. Read the story about Raj and Roy and answer the following questions:

a. How much did the bike cost?

• Raj bought the bicycle for ₹500.
• Answer: ₹500.

b. What is the amount that Roy returned after he got the job?

• Roy returned $₹500 + 0.1 \times 500$ = $₹500 + ₹50$ = ₹550.
• Answer: ₹550.

c. If Roy has $y$ amount left with him, what part of his salary did he give to Raj?

• Part of his salary given to Raj = $\frac{550}{25000}$.
• Answer: $\frac{550}{25000}$.

d. Form an equation using the expressions from parts a and b:

• Equation: $y + 550 = 25000$.
• Answer: $y + 550 = 25000$.

  Cambridge Math's Milestone Class 6th

By Prem Sir Math Solutions 9470710586