Tag: forming equations from statements

Questions Related to forming equations from statements

Henry just set up direct deposit from his employer to his checking account. The equation $\displaystyle y=360x-126.13$ represents the balance in Henry's account if he deposit his weekly paycheck for x weeks. Based on this equation, which of the following statements is true

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. Henry earns $126.13 per week.

  2. Henry made an initial deposit of $126.13.

  3. Before setting up the direct deposit, Henry had overdrawn his account.

  4. When Henry set up the direct deposit, he already has $360 in his account.

Show answer
Correct Option: C
Explanation:

The balance in Henry's account follows the relation $y = 360x - 126.13$, where $y$ is the balance in Henry's checking account and $x$ is the number of weeks passed. 

The difference in the balance between any two successive weeks is $ $360 $. This shows that Henry earns $ $360$ per week.
The other options can be checked simultaneously. After putting $x = 0$, we get $y = -126.13$. This shows that only option C is correct.

Ajit is $21$ years younger than his father. What is their total age in $7$ years time?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $(x + 28)$ years

  2. $(x + 35)$ years

  3. $(2x + 28)$ years

  4. $(2x + 35)$ years

Show answer
Correct Option: D
Explanation:
Let the age of Ajit be $x$ years.
$\therefore$ Age of Ajit's father $= x + 21$
After $7$ years-
Age of Ajit $= (x + 7)$ years
Age of Ajit's father $= x + 21 + 7 = x + 28$
Total age of Ajit and Ajit' father $= x + 7 + x + 28 = (2x + 35)$ years

Reema bought $x$ pens at Rs.$2.60$ each and $y$ greeting cards at $80$ paise each. If the pens cost Rs.$12$ more than the cards, the equation involving $x$ and $y$ is

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $13x-4y=6$

  2. $13x-4y=60$

  3. $260x-8y=100$

  4. $260x-8y=12$

Show answer
Correct Option: B
Explanation:

Given that Reema bought $x$ pens at Rs. $2.60$ each and $y$ greeting cards at $80$ paise each

Then cost of x pens $ =2.60 x$ RS 
And cost of y greeting cards $=0.80 y$ Rs
But given that total cost of pens is Rs $12$ more than the cards

$\therefore 2.60 x=0.80 y+12$
Mltiply by 10 both sides we get
$2.60x\times 10=0.80y\times 10+12\times 10$
$\Rightarrow 26x=8y+120$
$\Rightarrow 26x-8y=120$
Divided by 2 both sides we get
$13x-4y=60$

Equation for the statement 'Thrice the length ($l$) of a room is $340$ metres' is _____ .

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $3l=430$

  2. $3l=340$

  3. $3+l=340$

  4. $3l+340=0$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$   The length of room is $l$.

$\Rightarrow$   So, thrice the length means $3l$.
$\therefore$    According to the statement given in question,
$\Rightarrow$  $3l=340$

Ashima bought $23$ things from the market. She bought five more jeans than shirts and two fewer watches than jeans. If $x$ represents the number of shirts in total, then which sentence can be used to find how many of each thing are bought?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $x + (x + 5) + (x + 3) = 23$

  2. $x + (x - 5) + (x - 3) = 23$

  3. $(x + 5) + (x + 3) = 23$

  4. $x + (x + 3) = 23$

Show answer
Correct Option: A
Explanation:

Given: Number of shirts = $x$ 

Number of Jeans = $x+5$
Number of watches= $(x+5)-2=x+3$
$\therefore$  According to question,
$x+(x+5)+(x+3)=23$

You are decorating a gift pack with 15 flowers. You want an equal number of flowers in each of the 3 rows on the gift pack. Which equation would you use to find the number of flowers, r, in each row?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. r + 3 = 15

  2. 15 + r = 3

  3. 3r = 15

  4. $\dfrac {3}{r}$ = 15

Show answer
Correct Option: C
Explanation:

We have to decorate a gift pack with 15 flowers. 

$\Rightarrow$  There are 3 rows on gift pack and we want equal number of flowers in each row.
$\Rightarrow$  Let $r$ be number of flowers in each row.
$\therefore$   Number of rows $\times$ Number of flowers in each row = Number of flowers.
$\Rightarrow$  $3\times r=15$
$\therefore$     $3r=15$

A shopkeeper sells bananas in two types of boxes, one small and one large. A large box contains as many as 6 small boxes plus 2 loose bananas. Form an equation which gives the number of bananas in each small box, if the number of bananas in 1 large box is 50.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 3x + 1 = 50

  2. x + 1 = 20

  3. 6x + 2 = 50

  4. 2x + 1 = 20

Show answer
Correct Option: C
Explanation:
 Let the number of bananas in each small box be $x.$
$\Rightarrow$  Number of small boxes $=6$
$\therefore$   According to question, $6x + 2 = 50$

The teacher tells the class that the highest marks obtained by a student in her class is four times the lowest marks plus 6. The highest score is 65. Form the equation which will calculate the lowest marks.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 6m + 4 = 65

  2. 4m + 65 = 6

  3. 4m + 6 = 65

  4. 6m + 65 = 4

Show answer
Correct Option: C
Explanation:
 Let the lowest marks obtained by a student be $m.$
$\Rightarrow$  The highest score is $65.$
$\Rightarrow$  According to question, $4m+6=65$
$\therefore$   The equation to calculate lowest marks is $4m+6=65$.

Ram's father's age is 3 years more than two times Ram's age. Ram's father is 45 years old. Form an equation to find Ram's age.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 2x + 3 = 45

  2. 3x + 2 = 45

  3. 6x + 3 = 45

  4. 5x + 1 = 45

Show answer
Correct Option: A
Explanation:
 Let Ram's age be $x$ years.
$\Rightarrow$  Ram's father's age = $(2x + 3)$ years
$\therefore$    According to question, $2x + 3 = 45$

A group of students decided to collect as many paise from each member of the group as is the number of members in the group. If the total collection amounts to Rs.$22.09$, the number of members in the group is.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $37$

  2. $47$

  3. $39$

  4. $49$

Show answer
Correct Option: B
Explanation:

Let the total number of members = $x$


So, money collected from each member = $x\ paise=Rs.\ 0.01x$

Total money collected = $x\times0.01x=0.01\ x^2$

$\Rightarrow0.01\ x^2=22.09$

$\Rightarrow x^2=\dfrac{22.09}{0.01}=2209$

$\Rightarrow x=\sqrt{2209}=47$

So, there are  $47$  members in the group.   $[B]$