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Sagot :
Let's break down the solution to answer each part of the question step-by-step:
a) i. The number of students who passed Mathematics:
The number of students who passed Mathematics is \( \mathbf{30} \).
ii. The number of students who passed Science:
The number of students who passed Science is \( \mathbf{25} \).
iii. The number of students who passed exactly one of the two subjects:
The number of students who passed exactly one of the two subjects is \( \mathbf{10} \).
b) i) Finding the value of \( x \) given the exterior angles of a polygon:
The exterior angles of a polygon are given as \( 25^\circ \), \( 43^\circ \), \( 142^\circ \), \( 4x^\circ \), and \( x^\circ \).
The sum of all exterior angles of any polygon is always \(360^\circ\). Hence, we can set up the equation:
[tex]\[ 25^\circ + 43^\circ + 142^\circ + 4x^\circ + x^\circ = 360^\circ \][/tex]
Combining like terms, we get:
[tex]\[ 210^\circ + 5x^\circ = 360^\circ \][/tex]
Solving for \( x \):
[tex]\[ 5x^\circ = 150^\circ \][/tex]
[tex]\[ x = \frac{150^\circ}{5} = 30^\circ \][/tex]
So, the value of \( x \) is \( \mathbf{30^\circ} \).
b) ii) Rachael's textbook order:
Rachael wants to order textbooks online, where:
- Each textbook costs \( Gh \)
- The shipping cost for the entire order is \( Ghc 30.00 \)
- Rachael has no more than \( Ghc 530.00 \)
(a) Write an inequality that represents Rachael's situation:
Let \( n \) represent the number of textbooks Rachael can order. The total cost of the textbooks plus the shipping cost should be less than or equal to her budget, i.e.,
[tex]\[ n \cdot Gh + 30 \leq 530 \][/tex]
(β) How many textbooks can Rachael order without exceeding her Ghc 530.00 limit?
First, set up the inequality:
[tex]\[ n \cdot Gh + 30 \leq 530 \][/tex]
Subtracting 30 from both sides:
[tex]\[ n \cdot Gh \leq 500 \][/tex]
Dividing both sides by the cost per textbook \( Gh \):
[tex]\[ n \leq \frac{500}{Gh} \][/tex]
Thus, the number of textbooks Rachael can order without exceeding her budget is \( \mathbf{\frac{500}{Gh}} \).
c) Selling price of the car:
A man bought a car for \( Ghc 15,000.00 \) and sold it at a profit of 20%. To find the selling price:
The profit amount is:
[tex]\[ \text{Profit amount} = 15,000 \times \frac{20}{100} = 3,000 \][/tex]
The selling price is then:
[tex]\[ \text{Selling price} = \text{Purchase price} + \text{Profit amount} = 15,000 + 3,000 = 18,000 \][/tex]
So, the selling price of the car is [tex]\( \mathbf{Ghc 18,000.00} \)[/tex].
a) i. The number of students who passed Mathematics:
The number of students who passed Mathematics is \( \mathbf{30} \).
ii. The number of students who passed Science:
The number of students who passed Science is \( \mathbf{25} \).
iii. The number of students who passed exactly one of the two subjects:
The number of students who passed exactly one of the two subjects is \( \mathbf{10} \).
b) i) Finding the value of \( x \) given the exterior angles of a polygon:
The exterior angles of a polygon are given as \( 25^\circ \), \( 43^\circ \), \( 142^\circ \), \( 4x^\circ \), and \( x^\circ \).
The sum of all exterior angles of any polygon is always \(360^\circ\). Hence, we can set up the equation:
[tex]\[ 25^\circ + 43^\circ + 142^\circ + 4x^\circ + x^\circ = 360^\circ \][/tex]
Combining like terms, we get:
[tex]\[ 210^\circ + 5x^\circ = 360^\circ \][/tex]
Solving for \( x \):
[tex]\[ 5x^\circ = 150^\circ \][/tex]
[tex]\[ x = \frac{150^\circ}{5} = 30^\circ \][/tex]
So, the value of \( x \) is \( \mathbf{30^\circ} \).
b) ii) Rachael's textbook order:
Rachael wants to order textbooks online, where:
- Each textbook costs \( Gh \)
- The shipping cost for the entire order is \( Ghc 30.00 \)
- Rachael has no more than \( Ghc 530.00 \)
(a) Write an inequality that represents Rachael's situation:
Let \( n \) represent the number of textbooks Rachael can order. The total cost of the textbooks plus the shipping cost should be less than or equal to her budget, i.e.,
[tex]\[ n \cdot Gh + 30 \leq 530 \][/tex]
(β) How many textbooks can Rachael order without exceeding her Ghc 530.00 limit?
First, set up the inequality:
[tex]\[ n \cdot Gh + 30 \leq 530 \][/tex]
Subtracting 30 from both sides:
[tex]\[ n \cdot Gh \leq 500 \][/tex]
Dividing both sides by the cost per textbook \( Gh \):
[tex]\[ n \leq \frac{500}{Gh} \][/tex]
Thus, the number of textbooks Rachael can order without exceeding her budget is \( \mathbf{\frac{500}{Gh}} \).
c) Selling price of the car:
A man bought a car for \( Ghc 15,000.00 \) and sold it at a profit of 20%. To find the selling price:
The profit amount is:
[tex]\[ \text{Profit amount} = 15,000 \times \frac{20}{100} = 3,000 \][/tex]
The selling price is then:
[tex]\[ \text{Selling price} = \text{Purchase price} + \text{Profit amount} = 15,000 + 3,000 = 18,000 \][/tex]
So, the selling price of the car is [tex]\( \mathbf{Ghc 18,000.00} \)[/tex].
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