Joel can read around 16 sentences per minute of his current novel. He wants to finish his reading before the movie comes out nex
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i ) 3(2x - 3) = 4(2x + 4)
ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2. 3x /4 - 7 /4 = 5x + 12
cancel 4 from both sides
3. x +7 - 8x/3 = 17/6 - 5x/8
put x = 4
L.H.S. = R.H.S.
<h2>--------------------</h2>4. Let 3 consecutive integers : x , x+1 , x+2
As per the question : 2x + 3(x+1) + 4(x+2) = 56
9x + 11 = 56
Transpose 11 to RHS
9x = 45
Divide both sides by 9
x = 5 ,
x + 1 = 5 + 1 = 6
x + 2 = 5 + 2 = 7
Numbers are 5 , 6 and 7 .
<h2>-----------------------</h2>5. Let the age of Jane’s younger sister is x.
Age of Jane will be x + 6
As per the question, after 10 years the sum of their ages will be 50.
After 10 years,
age of Jane = x + 16
age of her younger sister = x + 10
Therefore,
x + 16 + x +10 = 50
2x + 26 = 50
2x = 24
x = 12
Thus, the present age of Jane’s younger sister is 12 years.
And of Jane’s is 12 + 6 = 18 years.
<h2>---------------------</h2>6. Let the breadth of rectangular swimming pool be x metres.
Then, its length = (2x + 2) metres.
We know that the Perimeter of a rectangle
= 2(Length + Breadth)
= 2(2x + 2 + x) = 6x + 4
According to the given condition, we have
6x + 4 = 154
6x = 154 − 4
6x = 150
[Dividing both sides by 6]
x = 25
Thus, breadth = 25 m and
length = 25 × 2 + 2 = 52 m .
<h2>---------------------</h2>7. Let the digit in ten's .
Place be x and the digit in the one's place be y.
x − y = 5 ⟶ (i)
Two digit number = 10x + y
Two digit after reversing the digits = 10y + x
According to question ,
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 9 ⟶ (ii)
On adding (i) and (ii),
2x = 14
x = 7
Putting the value of x in equation (i)
x − y = 5
y = 2
Number = 10x + y
=72 .
<h2>-----------------------</h2>8. Let the speed of the steamer in still water be x km/h.
Then , the speed downstream = (x+2) km/h
and the speed upstream = (x−2) km/h
Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream
4(x + 2) = 5(x − 2)
4x + 8 = 5x − 10
4x − 5x = − 10 − 8
[Transposing 5x to LHS and 8 to RHS]
−x = −18 or x = 18 km/h .
<h2>-----------------------</h2>9. Let the number of notes of different denomination be x.
∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.
Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x
Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x
Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x
As per the question
Total amount = 400000
200x + 150x + 50x = 400000
400x = 400000 , x = 1000
No of Rs 100 notes = 2x = 2 × 1000 = 2000
No of Rs 50 notes = 3x = 3 × 1000 = 3000
No of Rs 10 notes = 5x = 5 × 1000 = 5000 .
<h2>------------------------</h2>10. Let the age of the man be x
Then age of his son becomes (x − 24)
2 years later from now,
Age of man will be = x + 2
and age of his son will be = (x − 24 + 2) = x − 22
According to question,
2(x − 22) = x + 2
i.e., 2x − 44 = x + 2
i.e., x = 46
Therefore ,
Present age of man = 46 years
And present age of his son = 46 − 24 = 22 years .
Answer:
For<em> </em>38 roses at <em>$5.15</em> per rose, Florist A is Less Expensive then Florist B
For<em> </em>34 roses at <em>$5.20</em> per rose, Florist A is Less Expensive then Florist B
Step-by-step explanation:
The Full Question Reads:
<u><em>Derek wants to order some roses online. Florist A charges $4.75 per blue rose plus $40 delivery charge. Florist B charges $5.15 per red rose plus $25 delivery charge. If Florist B increases the cost per rose to $5.20, for what number of roses is it less expensive to order from Florist A? From Florist B?</em></u>
To begin we need to understand our given information and what we are actually looking for.
<u>Given Information</u>
Florist A:
charges $4.75 per blue rose
charges $40 per delivery
Florist B:
charges $5.15 per red rose
charges $25 per delivery
Note: in this problem we ignore the colour of the rose (red or blue) as it does not affect our solution or contributes to it. Therefore we shall call our first variable representing the number of roses as .
The next step is to construct a system of equations representing our problem and our given information. Here we are looking at linear relationships so a linear function of the form:
Eqn(1).
<em>will suffice where</em>
: represents the total cost from the Florists (i.e. number of roses and delivery charges). Dependent Variable
: represents the number of roses purchased from the Florists. Independent Variable
: is our relationship factor between
and
: is our constant which in this problem is the <em>delivery charge</em> value for each florist.
Since we have two Florists, we will construct two equations, one for each florist, by employing Eqn(1). and our given information as follow:
Florist A: Eqn(2).
Florist B: Eqn(3).
By employing both equations above and writing them as an inequality <em>since we are looking for which value of </em><em> (i.e. number of roses) will the less expensive Florist be and then solving for </em>
<em> we have: </em>
<em></em>
<em> Gathering all similar terms together</em>
<em> Simplifying</em>
<em> Solving for x </em>
<em></em>
<em>(note how < changes to > since any multiplication/devision process of negative sign in an Inequality will change the order of < to > and vice versa). </em>
Since a rose has to be sold as a whole and not half we will say that <em></em> So we can then plug in the value of
in Eqn(2) and Eqn(3) and find the cost of buying more than 38 roses from each:
Eqn(2): Florist A:
Eqn(3): Florist B:
Which tells us that Florist A is less expensive than Florist B by $0.20 for a purchase of more than 38 roses.
Next the question tells us that Florist B increases the cost from $5.15 to $5.20 per rose, which in Eqn(3) denotes our value and thus Eqn(3). now becomes:
Florist B: Eqn(3).
Applying the same method like before and solving for the value of <em> we have: </em>
<em></em>
<em> Gathering all similar terms together</em>
<em> Simplifying</em>
<em> Solving for x </em>
<em></em>
Similarly as a rose has to be sold as a whole and not half we will say that <em></em> So we can then plug in the value of
in Eqn(2) and Eqn(3) and find the cost of buying more than 34 roses from each:
Eqn(2): Florist A:
Eqn(3): Florist B:
Which tells us that Florist A is again less expensive than Florist B by $0.30 for a purchase of more than 34 roses. It was also shown that as the cost of the rose increased by $0.05 the number of roses for purchase decreased.