[2 Mark Question Answer]

Question 12 Marks

A number is as much greater than 35 as is less than 53. Find the number.

Answer

Let the number $=x$
According to the condition
$ \begin{aligned} & x-35=53-x \\ & \Rightarrow x+x=53+35 \\ & \Rightarrow 2 x=88 \end{aligned} $
$ \Rightarrow x=\frac{88}{2}=44 $
$\therefore$ Number $=44$

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Question 22 Marks

The sum of twice a number and 4 is 80, find the number.

Answer

Let the number $=x$
According to the condition
$ \begin{aligned} & 2 x+4=80 \\ & \Rightarrow 2 x=80-4 \\ & \Rightarrow 2 x=76 \\ & \Rightarrow x=\frac{76}{2}=38 \end{aligned} $
$ \text { Number }=38 $

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Question 32 Marks

If 15 is added to a number, the result is 69, find the number.

Answer

Let the number = x
According to the condition
x + 15 = 69
⇒ x = 69 – 15 x = 54
∴Number = 54

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Question 42 Marks

Six times a number is 72, find the number.

Answer

Let the number $=x$
According to the condition
$ 6 x=72 $
$ \Rightarrow x=\frac{72}{6} $
$ \Rightarrow x=12 $
$\therefore$ Number $=12$

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Question 52 Marks

One-fifth of a number is 5, find the number.

Answer

Let the number $=x$
According to the condition
$ \begin{aligned} & \frac{1}{5} x=5 \\ & \Rightarrow x=5 \times 5 \\ & \Rightarrow x=25 \end{aligned} $
$\therefore$ Number $=25$

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Question 62 Marks

Solve: $\frac{x}{3}-\frac{x}{4}=2$

Answer

$\begin{aligned} & \frac{x}{3}-\frac{x}{4}=2 \\ & \Rightarrow \frac{4 x-3 x}{12}=2 \\ & \Rightarrow 4 x-3 x=2 \times 12 \\ & \Rightarrow x=24\end{aligned}$

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Question 72 Marks

Solve: 10% of x = 20

Answer

$\begin{aligned} & 10 \% \text { of } x=20 \\ & \Rightarrow \frac{10}{100} \times x=20 \\ & \Rightarrow \frac{x}{10}=20 \\ & \Rightarrow x=20 \times 10=200 \\ & \therefore x=200\end{aligned}$

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Question 82 Marks

19x + 13 -12x + 3 = 23

Answer

$\begin{aligned} & 19 x+13-12 x+3=23 \\ & \Rightarrow 19 x-12 x=23-13-3 \\ & \Rightarrow 7 x=23-16=7 \\ & \Rightarrow x=\frac{7}{7}=1 \\ & \therefore x=1\end{aligned}$

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Question 92 Marks

24 = y + 2y + 3 + 4y

Answer

$\begin{aligned} & 24=y+2 y+3+4 y \\ & \Rightarrow 24-3=y+2 y+4 y \\ & \Rightarrow 21=7 y \\ & \Rightarrow 7 y=21 \\ & \Rightarrow y=\frac{21}{7}=3 \\ & \therefore y=3\end{aligned}$

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Question 102 Marks

9 + m = 6m + 8 – m

Answer

$\begin{aligned} & 9+m=6 m+8-m \\ & \Rightarrow m-6 m+m=8-9 \\ & \Rightarrow 2 m-6 m=-1 \\ & \Rightarrow-4 m=-1 \\ & \therefore m=\frac{-1}{-4}=\frac{1}{4}\end{aligned}$

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Question 112 Marks

4x – 5x + 2x = 28 + 3x

Answer

$\begin{aligned} & 4 x-5 x+2 x=28+3 x \\ & \Rightarrow 4 x-5 x+2 x-3 x=28 \\ & \Rightarrow 6 x-8 x=28 \\ & \Rightarrow x=\frac{28}{-2}=-14\end{aligned}$
$\therefore x=-14$

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Question 122 Marks

8 – 7x = 13x + 8

Answer

$\begin{aligned} & 8-7 x=13 x+8 \\ & \Rightarrow-7 x-13 x=8-8 \\ & \Rightarrow-20 x=0 \\ & \Rightarrow x=\frac{0}{-20}=0\end{aligned}$
$\therefore \mathrm{x}=0$

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Question 132 Marks

6 = 7 + 2p -5

Answer

$\begin{aligned} & 6=7+2 p-5 \\ & \Rightarrow-2 p=7-5-6 \\ & \Rightarrow-2 p=-4 \\ & \Rightarrow p=\frac{-4}{-2}=2 \\ & \therefore p=2\end{aligned}$

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Question 142 Marks

6b + 40 = – 100 – b

Answer

$\begin{aligned} & 6 b+40=-100-b \\ & \Rightarrow 6 b+b=-100-40 \\ & \Rightarrow 7 b=-140 \\ & \Rightarrow b=\frac{-140}{7}=-20 \\ & \therefore b=-20\end{aligned}$

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Question 152 Marks

8y – 4y = 20

Answer

$\begin{aligned} & 8 y-4 y=20 \\ & \Rightarrow 4 y=20 \\ & \Rightarrow y=\frac{20}{4}=5 \\ & \therefore y=5\end{aligned}$

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Question 162 Marks

Solve the following equation:
2b – 14 = 8

Answer

$\begin{aligned} & 2 b-14=8 \\ & \Rightarrow 2 b=8+14=22 \\ & \Rightarrow b=\frac{22}{2}=11 \\ & \therefore b=11\end{aligned}$

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Question 172 Marks

Solve the following equation:
9y -7 = 20

Answer

$9 y-7=20$
$ \Rightarrow 9 y=20+7=27 $
$ \Rightarrow \mathrm{y}=\frac{27}{9}=3 $
$ \therefore y=3 $

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Question 182 Marks

Solve the following equation:
3p – 1 = 8

Answer

$\begin{aligned} & 3 p-1=8 \\ & \Rightarrow 3 p=8+1=9 \\ & \Rightarrow p=\frac{9}{3}=3 \\ & \therefore p=3\end{aligned}$

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Question 192 Marks

Solve the following equation:
2a – 3 =5

Answer

$\begin{aligned} & 2 a-3=5 \\ & \Rightarrow 2 a=5+3 \\ & \Rightarrow 2 a=8 \\ & \Rightarrow a=\frac{8}{2}=4\end{aligned}$
→ a = 4

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Question 202 Marks

Solve the following equation:
$\frac{3}{16} \mathrm{~m}=21$

Answer

$\begin{aligned} & \frac{3}{16} \mathrm{~m}=21 \\ & \Rightarrow 3 \mathrm{~m}=21 \times 16=336 \\ & \Rightarrow \mathrm{m}=\frac{336}{3}=112 \\ & \therefore \mathrm{m}=112\end{aligned}$

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Question 212 Marks

Solve the following equation:
$\mathrm{p}-12=2 \frac{2}{3}$

Answer

$\begin{aligned} & \mathrm{p}-12=2 \frac{2}{3} \\ & \Rightarrow \mathrm{p}-12=\frac{8}{3} \\ & \Rightarrow \mathrm{p}=\frac{8}{3}+\frac{12}{1}=\frac{8+36}{3}=\frac{44}{3} \\ & \therefore \mathrm{p}=\frac{44}{3}=14 \frac{2}{3}\end{aligned}$

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Question 222 Marks

Solve the following equation:
p + 0.02 = 0.08

Answer

p + 0.02 = 0.08
⇒ p = 0.08 – 0.02 = 0.06
∴ p = 0 06

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Question 232 Marks

Solve the following equation:
$x+\frac{1}{4}=-\frac{3}{8}$

Answer

$\begin{aligned} & x+\frac{1}{4}=-\frac{3}{8} \\ & \Rightarrow x=-\frac{3}{8}-\frac{1}{4}=\frac{-3-2}{8}=-\frac{5}{8} \\ & \therefore x=\frac{-5}{8}\end{aligned}$

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Question 242 Marks

Solve the following equation:
4 = x - 2.5

Answer

4 = x - 2.5
⇒4 + 2.5 = x
⇒ 6.5 = x
∴ x = 6.5

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Question 252 Marks

Solve the following equation:
12 = c – 2

Answer

12 = c – 2
⇒ 12 + 2 = c
⇒ 14 = c
∴ c = 14

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Question 262 Marks

Solve the following equation:
$\frac{a}{15}-2=0$

Answer

$\begin{aligned} & \frac{\mathrm{a}}{15}-2=0 \\ & \Rightarrow \frac{\mathrm{a}}{15}=2 \\ & \Rightarrow \mathrm{a}=2 \times 15=30 \\ & \therefore \mathrm{a}=30\end{aligned}$

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Question 272 Marks

Solve the following equation:
$c-\frac{1}{2}=\frac{1}{3}$

Answer

$\begin{aligned} & c-\frac{1}{2}=\frac{1}{3} \\ & c=\frac{1}{3}+\frac{1}{5}=\frac{2+3}{6}=\frac{5}{6} \\ & \therefore c=\frac{5}{6}\end{aligned}$

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Question 282 Marks

Solve the following equation:
10 + 6a = 40

Answer

$\begin{aligned} & 10+6 a=40 \\ & 10+6 a=40 \\ & \Rightarrow 6 a=40-10=30 \\ & \Rightarrow a=\frac{30}{6}=5 \\ & \therefore a=5\end{aligned}$

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Question 292 Marks